This case involves a dispute between a union representing professors at the University of Alaska and two professors who have not joined the union, object to paying union dues, and contest the manner in which the agency union fee for collective bargaining purposes is determined and collected.

BACKGROUND

Appellants Robert Carlson and John Morack are professors of the University of Alaska at Fairbanks. Appellants are part of a bargaining unit comprising teaching and research faculty at the University as set forth in a collective bargaining agreement between the University and United Academics-AAUP/AFT, AFL-CIO (“United Academics” or “the Union”). United Academics acts as bargaining agent and exclusive representative of Appellants and other members of the bargaining unit. The collective bargaining agreement requires all research and teaching faculty in the unit to maintain membership in the Union, or for those faculty members who choose to refrain from union membership, to pay mandatory “agency fees” as a condition of continued employment.

In March 1998, United Academics sent a letter to all nonmembers demanding that each professor tender “1.25% (.0125) of your bi-weekly salary with a $720 cap per calendar year.” The letter also advised:

To those nonmembers who failed to respond to the first demand letter, including Appellants, the Union repeated its demands in a letter dated April 21, 1998. The letter warned members that “[i]f the [dues checkoff authorization] form is not received by May 1, the next correspondence you will receive will be a letter informing you that United Academics has requested that the University terminate your employment per Article 4 of the Collective Bargaining Agreement.”

The letter also notified members that unless recipients authorized dues deductions by April 24, 1998, the Union would require payment of agency fees retroactive to January 1, 1998. Finally, the letter provided that if an employee failed to authorize automatic dues deductions by April 24, 1998, “United Academics will seek the collection of those fees through the courts and/or a collection agency regardless of the subsequent receipt of your fee deduction form or your future employment at the University of Alaska.”

On May 5, 1998, Appellants filed a verified class action under 42 U.S.C. § 1983 alleging violations of their First, Fifth, and Fourteenth Amendment rights. Appellants sought damages as well as declaratory and injunctive relief, equitable restitution, punitive damages, and attorneys’ fees and costs. Specifically, the complaint alleged that United Academics’ demands failed to provide the notice and procedural safeguards required by the United States Supreme Court in Chicago Teachers Union Local No. 1 v. Hudson, 475 U.S. 292 , 106 S.Ct. 1066 , 89 L.Ed.2d 232 (1986).

In August of 1998, Appellants filed a motion for class certification. The district court denied Appellants’ motion. Subsequently, Appellants filed a motion for summary judgment which the district court granted in part and denied in part. The court found as a matter of law, that the Union’s initial demands “clearly offended the notice and procedural safeguards mandated by Hudson.” Based on this finding, the district court concluded that Appellants were entitled to nominal damages and declaratory relief.

While the suit was pending before the district court, United Academics mailed two additional notices to members of the bargaining unit. On October 12, 1998, the Union sent a notice advising members that “[a]gency fees pursuant to the requirements of the United States Supreme Court decision Chicago Teachers Union v. Hudson will be initiated on November 15,1998. Any agency fees collected prior to November 15, 1998 will be reimbursed to individual faculty members.” Subsequently, on December 1, 1998, United Academics mailed to bargaining unit members documents that “were inadvertently omitted from the material accompanying the Chicago Teachers Union v. Hudson notice.”

On May 10, 1999, Appellants filed a renewed motion for summary judgment in which they challenged United Academics’ October and December demands. In re sponse, United Academics filed a motion for partial summary judgment. The parties disputed whether the December mailing cured, and therefore mooted, the admitted deficiencies of the October mailing. The district court concluded that because United Academics conceded the October notice was deficient and remedied the deficiency with the December mailing, the sufficiency of the notice should be determined by considering both the October and December mailings.

In addition, as relevant to this appeal, the district court found that United Academics’ subsequent demands (1) did not discriminate between those individuals who merely object to payment of full union dues and those individuals who object to payment of the dues and who wish to challenge the Union’s fee calculation before an impartial decisionmaker; and (2) did not violate Hudson by permitting an impartial decisionmaker to increase the fee amount. The court denied Appellants’ request for a permanent injunction finding that “it appears that the parties are now in virtual agreement regarding the form of notices to be sent in the future to comply with Hudson.” The court also granted United Academics’ motion for partial summary judgment, dismissing Appellants’ claims for punitive damages and injunctive relief.

On appeal, Appellants argue that the December notice violated Hudson because the notice (1) discriminates between objectors and challengers, and (2) allows the Union to seek an increased fee from nonmembers challenging its calculation. Appellants also contend that the district court erred when it treated their challenge to United Academics’ October notice as moot. Finally, Appellants challenge the district court’s denial of class certification.

The district court had jurisdiction pursuant to 18 U.S.C. §§ 1331 and 1343. We have jurisdiction pursuant to 28 U.S.C. § 1291 .

DISCUSSION

I. December Notice

We review a district court’s grant of summary judgment de novo. See Block v. City of Los Angeles, 253 F.3d 410, 416 (9th Cir.2001). We must determine, viewing the evidence in the light most favorable to the nonmoving party, whether there are any genuine issues of material fact and whether the district court correctly applied the relevant substantive law. See id.

It is well-settled that a nonunion member can be forced to share in the expenses incurred by a union in its role as the exclusive bargaining representative on behalf of employees. See Hudson, 475 U.S. at 301 , 106 S.Ct. 1066 . However, a union cannot, without infringing upon First Amendment rights, force nonmembers to pay for expenses related to political and ideological activities unrelated to the union’s duties as bargaining representative. See id. at 302 , 106 S.Ct. 1066 . In Hudson , the Supreme Court set forth three procedural requirements that a union must satisfy before collecting fees through an agency shop agreement. First, the union must provide nonmembers with an “adequate explanation” of the basis for calculating the agency fee so potential objectors can determine whether the fee is in fact fairly calculated. Id. at 310 , 106 S.Ct. 1066 . Second, if a nonmember objects to the agency fee calculation, the union’s procedure must provide “a reasonably prompt opportunity to challenge the amount of the fee before an impartial decisionmaker.” Id. Third, the union must create “an escrow for the amounts reasonably in dispute while such challenges are pending.” Id.

Appellants contend that two aspects of the Union’s procedures violate the Hudson requirements. First, Appellants argue that the Union’s two-class objection system discriminates between nonmembers who object to the agency fee but accept the Union’s reduced fee computation and those nonmembers who challenge the agency fee calculation. Second, Appellants argue that the Union’s procedural scheme, which allows the arbitrator to increase the agency fee, is designed to discourage nonmembers from challenging the amount of the fee and is unconstitutional.

A. Discrimination Between Challengers And Objectors

Under the Union’s procedures, professors who object to paying full union dues are offered two options: “Class I” Objection or “Class II” Objection. A “Class I Objecting Agency Fee Payer” is an employee in the collective bargaining unit who (1) does not choose to join United Academics; (2) objects to the use of his or her service fees for purposes unrelated to collective bargaining, contract administration and grievance adjustment; and (3) accepts the reduced agency fee as determined by United Academics. Upon receiving a Class I objection notice, United Academics promptly issues a rebate of the total amount in excess of the Union’s determined agency fee that had been deducted to date. Further refunds are made before dues are deducted or are unnecessary because the future monthly dues are reduced to the appropriate amount. Class I objectors waive their right to challenge the amount of the fee before an impartial arbitrator and may not have their fees reduced based on the outcome of another objector’s arbitration.

A “Class II Objecting Agency Fee Payer” is an employee in the collective bargaining unit who (1) does not choose to join United Academics; (2) objects to the use of his or her service fees for uses unrelated to collective bargaining, contract administration and grievance adjustment; and (3) objects to the reduced service fee as determined by United Academics. Under the Union’s procedure, a Class II objector requests that an impartial arbitrator promptly hear the objector’s challenge. If United Academics receives a timely Class II objection, the Union requests that the American Arbitration Association (“AAA”) appoint an independent arbitrator “to hold a hearing to determine the percentage of the union’s budget for the service fee year that will be expended for chargeable activities.” Class II objectors are required to agree that (1) the arbitrator may approve the Union’s calculations or increase or decrease the amount attributable to “non-ehargeable” activities; (2) the full amount of the agency fee that the Union receives will be retained in an interest-bearing escrow account until the arbitrator resolves the challenge; and (3) United Academics will thereafter transmit to the objector that amount of the fee attributable to “non-chargeable” activities as determined by the arbitrator, plus interest as appropriate.

Appellants contend that United Academics provides an immediate advance reduction to those professors who merely object but do not challenge the fee calculation (Class I objectors), while the Union denies an immediate advance reduction to those professors exercising their right to challenge its fee calculation (Class II objectors). Appellants allege that by doing so, United Academics intends to discourage challenges to the Union’s fee calculation. We disagree and conclude that the district court correctly rejected Appellants’ challenge to the procedures.

In reaching its decision, the district court relied upon Grunwald v. San Ber- nardino City Unified Sell. Dist., 994 F.2d 1370 (9th Cir.1993), in which this court upheld a similar procedure whereby dues were deducted and placed in an escrow pending resolution by an arbitrator. In Grunwald, nonunion teachers brought suit challenging a procedure in which the school district deducted one-tenth of the annual union dues for each of the ten months the teachers worked, regardless of whether the teacher was in the union or not. See id. at 1372. The union members’ deductions were sent to the unions while the agency fee payers’ deductions were placed in an interest bearing escrow account. See id. To receive a refund, nonmembers were required to submit a letter objecting to the union’s discretionary use of fees. See id. at 1373. Nonmembers could either accept the union’s calculations and receive a rebate for the entire year or dispute the union’s calculations and request that an arbitrator decide the percentage of the refund. See id. Plaintiffs challenged the “deduction-escrow-refund” procedure claiming the school district could not deduct more than what the union was entitled to receive for collective bargaining purposes, even temporarily. See id.

The court recognized that a system whereby full dues are removed and the objecting employee bears the burden of seeking a refund potentially burdens employees’ constitutional rights “unless the procedure serves a legitimate purpose and is administered in a fair and impartial fashion.” Id. at 1375. Yet, after reviewing the disputed procedure, the court concluded:

Id. at 1377.

The procedure at issue is similar to the procedure upheld in Grunwald. If a professor objects but accepts the computation of the reduced agency fee as determined by United Academics, regular monthly deductions of the full agency fee are taken from the objector’s salary, and the nonchargeable amount is either rebated by the Union or simply deducted from the objector’s monthly agency fee. If a professor objects but wishes to challenge the reduced agency fee as determined by United Academics, regular monthly deductions based upon the full agency fee are taken from the challenger’s salary and immediately placed into an interest bearing escrow account until an impartial arbitrator resolves the challenge. If the challenger prevails, he or she is entitled to the monetary value of any correction by the arbitrator. Thus, both challengers and objectors are subjected to regular monthly deductions based on the full agency fee and are entitled to a rebate of the nonchargeable amounts.

While it is true that challengers do not receive a rebate until the dispute is resolved by an impartial arbitrator, we conclude that the Union’s procedures comply with the Hudson standards. First, the procedures “provide for a reasonably prompt decision by an impartial decision-maker.” Hudson, 475 U.S. at 307 , 106 S.Ct. 1066 . Challengers have their objec tions “addressed in an expeditious, fair, and objective manner.” Id. Second, challengers’ fees are placed in an interest-bearing escrow account. Thus, there is no risk that challengers’ money can be used by the Union for non-representational purposes pending resolution of the challenge. See Grunwald, 994 F.2d at 1374. In addition, United Academics’ procedures provide for a reasonably prompt refund of the nonchargeable amounts. See id. at 1377. Finally, the Union has provided an “adequate explanation” for adopting the deduction-escrow-refund procedure at issue. Hudson, 475 U.S. at 309 , 106 S.Ct. 1066 . As the district court noted, the agency fee payers in the current action vary from year to year. The individual salaries do not go into effect until faculty members return in September to commence the work year. Prior to that time, the Union cannot easily contact new faculty members to determine if they wish to object or challenge the agency fees. Thus, we conclude that the deduction-escrow-refund procedure that United Academics has adopted for professors who challenge the Union’s computation of fees is “appropriately justified.” Grunwald, 994 F.2d at 1376. Accordingly, we reject Appellants’ challenge to the two-class objection system.

B. Arbitrator’s Ability to Increase Agency Fee

Appellants also object to the Union’s requirement that Class II objectors must agree that “the arbitrator may either approve the United Academics, AAUP/ AFT calculations or increase or decrease the amount attributable to ‘non-chargeable’ activities.” Appellants argue that a system which allows the Union to seek a higher chargeable percentage violates Hudson’s requirements.

The district court rejected Appellants’ argument and found that the system satisfied the Hudson requirements. We agree with the district court’s determination.

Appellants fail to articulate precisely how the provision violates Hudson . Under United Academics’ procedures, an impartial arbitrator is responsible for approving the Union’s calculations and determining whether the amounts attributable to nonchargeable activities should be adjusted upward or downward. Appellants contend that by allowing an arbitrator to increase the agency fee, United Academics seeks to chill an agency fee payer’s decision to challenge the fee determination. However, the arbitrator is appointed by the American Arbitration Association. Thus, the selection does not represent the Union’s unrestricted choice. See Hudson, 475 U.S. at 308 n. 21, 106 S.Ct. 1066 ; Grunwald, 994 F.2d at 1376. Further, both parties “may offer such evidence as they desire and shall produce such evidence as the arbitrator may deem necessary to an understanding and determination of the dispute.” American Arbitration Association, “Rules for Impartial Determination of Union Fees” (Jan. 1, 1988). We do not believe the Union could successfully influence a neutral arbitrator so as to prejudice the objectors. Instead, adjustments in the chargeable amount would likely occur only if the arbitrator finds an error in previous calculations. The adjustments can either increase or decrease the amount attributable to nonchargeable activities. Based on these factors, we conclude that the provision does not violate the Hudson requirements.

II. October Notice

We review a district court’s determination of mootness de novo. See Knight v. Kenai Peninsula Borough Sch. Dist., 131 F.3d 807 , 811 (9th Cir.1997).

On appeal, Appellants argue that the district court erred when it treated United Academics’ remedial measures, subsequent to its October mailing, as mooting their claim that the October demand, standing alone, violates the Hudson requirements. Appellants contend that because the court agreed the October demand is constitutionally inadequate when standing alone, it erred when it failed to enter a judgment declaring it to be so. Appellants maintain that United Academics remains free to return to the inadequate notice procedure employed by the Union in October.

The district court recognized that in Hudson , the Supreme Court rejected an argument that a union’s alteration of its notice procedures after trial mooted alleged deficiencies in the union’s notice procedures. Notwithstanding Hudson , the court concluded there was little concern that United Academics would fail to provide complete notice in the future, as the Union had readily conceded the October notice was inadequate and had subsequently mailed a notice in compliance with Hudson .

It is undisputed that as a general rule “[v]oluntary cessation of challenged conduct moots a ease ... only if it is ‘absolutely clear that the allegedly wrongful behavior could not reasonably be expected to recur.’ ” Adarand Constructors, Inc. v. Slater, 528 U.S. 216, 222 , 120 S.Ct. 722 , 145 L.Ed.2d 650 (2000) (quoting United States v. Concentrated Phosphate Export Ass’n, 393 U.S. 199, 203 , 89 S.Ct. 361 , 21 L.Ed.2d 344 (1968)). Although the burden of demonstrating mootness is a heavy one, see id., we find that the burden is fully met on this record.

In the current action, United Academics mailed the October and December 1998 notices prior to the district court’s disposition of Appellants’ first summary judgment motion challenging the earlier notices. Because Appellants’ initial complaint did not address the October and December mailings, the court’s first order, dated February 16, 1999, only addressed Appellants’ challenge to the earlier notices. The court declined Appellants’ request to review the subsequent mailings absent the filing of a supplemental pleading “setting forth the events which have transpired since the filing of their complaint.”

Based on the district court’s statement, Appellants filed a renewed motion for summary judgment on May 10, 1999, in which they challenged the October and December notices. Many of the arguments in Appellants’ motion focused on the insufficiency of the October mailing without reference to the material provided in the December mailing. However, when the district court considered and ruled on Appellants’ renewed motion for summary judgment, the Union had conceded many months prior that the October notice was inadequate and had distributed the omitted material to all objectors in an attempt to comply with Hudson . Thus, the procedure as presented to the district court included both the admittedly deficient October demand and the amended December demand.

We conclude that the district court did not err in declining Appellants’ request to grant declaratory and injunctive relief as to the October notice. It is unreasonable to think that the Union would resort to conduct that it had admitted in writing was constitutionally deficient and had attempted to correct over fourteen months prior to the district court’s disposition of Appellants’ challenge. In fact, the Union was attempting to comply with the Hudson standards several months before the dis trict court filed its first order in which the court reviewed United Academics’ initial demands and concluded they were constitutionally inadequate. We do not believe United Academics would now attempt to revert to the deficient notice format and subject itself to future litigation that it would clearly lose. Under these circumstances, we hold that the conceded defect was cured, and therefore mooted, by the Union’s actions, and the district court correctly rejected Appellants’ request for declaratory and injunctive relief.

III. Class Certification

Appellants challenge the district court’s denial of class certification. Because we affirm the district court judgment for the Union on the merits, class certification would serve no purpose. Thus, we do not consider whether the district court abused its discretion in denying Appellants’ motion for class certification.

AFFIRMED

. With the October notice, United Academics attached a document titled "Schedule of Expenses and Allocation between Chargeable and Nonchargeable Expenses,” which disclosed that United Academics made payment to the American Association of University Professors ("AAUP”), American Federation of Teachers ("AFT”), and Alaska Public Employees Association/AFT ("APEA/AFT”). . With the December notice, United Academics provided copies of the American Arbitration Association's Rules for Impartial Determination of Union Fees, the AAUP’s "Allocation of Expenses-Fee Rebate,” the AFT’s statement discussing "allocation between chargeable expenses and nonchargeable expenses,” and the APEA/AFT's independent auditor's report discussing chargeable and nonchargeable expenses.