While President Donald Trump vows to press ahead with efforts to overturn the election, judges across the country have consistently swatted down his legal challenges.

Trump's campaign has failed to make any real headway in court without proof of widespread fraud, which experts widely agree doesn't exist. Over the course of a single day this week, Trump and his Republican allies dropped or lost cases seeking to block the certification of election results in three different states.

Experts say Trump won't succeed in stopping President-elect Joe Biden from taking office in January. But his repetition of baseless claims that the race was rigged is undermining public confidence in the election system while instilling in his supporters the idea that Biden will be an illegitimate president.

Where Republican election challenges stand in six states:

ARIZONA

THE CASE: The Arizona Republican Party had tried to block the certification of the election results in the state’s most populous county, Maricopa, until a court ruled on the party’s lawsuit asking for a new hand count of a sampling of ballots. An audit already completed by the county found no discrepancies, officials said.

WHAT HAPPENED: A judge on Thursday rejected Republicans' bid to postpone the certification of election results and dismissed the party’s legal challenge that sought a new audit of a sampling of ballots. Judge John Hanna provided no explanation, except to say that the GOP’s request to amend its lawsuit was futile, and barred the party from refiling the case. The judge promised a full explanation in the future.

In a separate case, Trump’s campaign and the Republican National Committee also had sought to delay the certification of election results in Maricopa County. In that case, they asked for the manual inspection of ballots in metro Phoenix, alleging that some votes were improperly rejected. A judge dismissed the case on Nov. 13 after the campaign’s lawyers acknowledged the small number of ballots at issue wouldn’t change the outcome of how Arizona voted for president. Maricopa County leaders certified election results Friday.

GEORGIA

THE CASE: A high-profile conservative attorney, L. Lin Wood Jr., sued in an attempt to block the certification of election results in Georgia. Wood alleges Georgia illegally changed the process for handling absentee ballots. Wood's lawsuit takes aim at a legal settlement signed earlier this year that addresses accusations about a lack of statewide standards for judging signatures on absentee ballot envelopes. Georgia’s deputy secretary of state has called Wood’s case a “silly, baseless claim.”

WHAT HAPPENED: A judge on Thursday denied Wood's request for a temporary restraining order to halt certification. Georgia Gov. Brian Kemp certified the state's slate of electors Friday. Trump has until the end of the day Tuesday to request a recount.

MICHIGAN

THE CASE: Trump’s campaign sued in an attempt to block the certification of election results in the state, alleging that election officials “allowed fraud and incompetence to corrupt the conduct of the 2020 general election.” Trump’s legal team alleged that its observers were prevented from being able to properly watch the vote counting, that ineligible ballots were counted and that Republican challenges to ballots were ignored.

Another lawsuit filed this week on behalf of two poll challengers asked a court to halt the certification of election results until an independent audit is completed to “ensure the accuracy and integrity of the election."

WHAT HAPPENED: The Trump campaign dropped its case Thursday, citing statements from Republican Wayne County canvassers who initially blocked certification of election results in Michigan’s largest county before approving them on Tuesday. The two canvassers now say they want to change their position again, but officials say there’s no way for them to rescind their vote.

Lawyers for the two poll challengers also abruptly withdrew their lawsuit this week with no explanation.

NEVADA

THE CASE: Trump’s campaign is asking a judge to nullify Nevada’s election results or set them aside and declare him the winner, arguing that illegal or improper votes were cast and the use of optical scanning to process signatures on mail-in ballots violated state law. The Trump lawsuit, filed Tuesday, rehashes arguments that judges in Nevada and elsewhere have already rejected. It claims that votes were cast on behalf of dead people, that election observers weren’t allowed to witness “key points” of processing and that people on American Indian territories were illegally given incentives to vote.

In a separate court filing, a voting watchdog group led by a conservative former state lawmaker wanted a judge to block statewide certification of the election.

WHAT HAPPENED: A judge on Friday rejected the voting watchdog group's bid to block statewide certification. A hearing in the Trump campaign challenge is scheduled Dec. 1.

PENNSYLVANIA

THE CASE: A Trump campaign case aims to stop the state from certifying the election, alleging Philadelphia and six counties wrongly allowed voters to correct problems with mail-in ballots that were otherwise going to be disqualified for a technicality, like lacking a secrecy envelope or a signature. The total number of affected ballots was not expected to come anywhere close to Biden’s margin of more than 80,000 votes.

WHAT HAPPENED: Trump’s personal lawyer, Rudy Giuliani, signed onto the case this week after others abruptly withdrew, and the former New York City mayor argued in court on Tuesday for the first time since the 1990s. Giuliani made wild, unsupported allegations of a nationwide conspiracy by Democrats to steal the election. The judge did not immediately issue a ruling and canceled a hearing that was set for Thursday but set out a schedule for both sides to make new filings this week.

WISCONSIN

THE CASE: Trump’s campaign on Wednesday filed for a recount in the counties that cover Milwaukee and Madison, both Democratic strongholds. It alleged — again without evidence — that absentee ballots were illegally altered or issued and that government officials violated state law.

WHAT HAPPENED: Biden won Wisconsin by 20,600 votes. The recount of the presidential election in the state's two most heavily Democratic counties began Friday with Trump’s campaign seeking to discard tens of thousands of absentee ballots that it alleged should not have been counted. Trump’s three objections attempting to discard the ballots were denied by the three-member Dane County Board of Canvassers. Trump was expected to make the same objections in Milwaukee County ahead of a court challenge once the recount concludes, perhaps as soon as Wednesday.

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Associated Press writers Jacques Billeaud in Phoenix, Marc Levy in Harrisburg, Pa., Ken Ritter in Las Vegas, Kate Brumback in Atlanta and Scott Bauer in Madison, Wis., contributed to this report.