Giuliani peddles election conspiracy theories and falsehoods.

Rudolph W. Giuliani, President Trump’s personal lawyer, has spread a litany of falsehoods and conspiracy theories in media appearances and social media over the past week.

Mr. Giuliani, who has a long history of fudging the truth and who has led the Trump campaign’s largely unsuccessful legal fight over the election, has focused particularly on debunked claims of barred poll workers and unsubstantiated conspiracy theories about a voting software company affecting the election’s outcome.

Debunked claims about poll workers

In interviews on Fox News, Mr. Giuliani has repeatedly claimed that Democratic officials blocked Republican poll watchers from observing ballot counting in “10 different crooked Democratic cities,” including Philadelphia, Pittsburgh, Detroit, Milwaukee, Reno, Phoenix and Atlanta. And in the counties where Philadelphia and Pittsburgh are, he has said, the lack of access affected over 680,000 votes.

There’s no evidence to support any of these allegations. Mr. Trump’s own legal filings acknowledged the presence of Republican observers in Nevada, Pennsylvania, Georgia and Arizona and there were at least 134 Republican poll challengers present inside TCF Center in Detroit, a convention center where votes were counted.

Mr. Giuliani has brought up Philadelphia and Pittsburgh several times. That’s because a Trump campaign lawsuit had claimed that some 682,000 ballots in those cities’ two counties were processed “when no observation was allowed” and sought to have those votes thrown out.

But as The Washington Post and The Associated Press have reported, and as Mr. Giuliani said in court on Tuesday, the Trump campaign recently revised its lawsuit and withdrew this particular claim.

“My judgment is that when Hillary Clinton said to Biden about four weeks ago don’t concede no matter what, she meant even if you’re behind by 800,000 votes in Pennsylvania, Joe, don’t worry, we’ll fix it for you,” Mr. Giuliani misleadingly said on Nov. 9. (Mrs. Clinton did not say Mr. Biden should “never” concede, but rather he shouldn’t on election night because counting mail-in ballots could “drag out” for days.)

Conspiracy theories about a software company

Mr. Giuliani has also accused Dominion Voting Systems, a voting software company, of having foreign, and seemingly nefarious ties.

The company, he has said in several Fox News appearances, is associated with those who were “very close” to two Venezuelan presidents, Hugo Chávez and Nicolás Maduro, as well as the billionaire financier George Soros, because it is “owned by another company called Smartmatic.”

That is wrong. Smartmatic has said it has never owned shares, had financial stakes or provided software or technology to Dominion. Dominion’s chief executive said in an April letter to Congress that he owned a 12 percent stake of the company, while a private equity firm, Staple Street Capital Group in New York, owned about 76 percent. (No other investor held more than 5 percent of Dominion.)

Smartmatic previously owned a voting machine company, Sequoia Voting Systems, before selling it in 2007, as the Washington Post Fact Checker reported. Dominion purchased some assets from Sequoia Voting Systems in 2010.

Smartmatic itself was founded in Florida, incorporated in the United States and based in London. It overhauled Venezuela’s election machinery in 2004 and took out a loan from the country. In the 2017 election there, the company said the Venezuelan government falsified turnout figures. That led the government to reject its claims and threaten legal action, undermining Mr. Giuliani’s claims that Smartmatic was “close” with Mr. Maduro.

Smartmatic’s connection to Mr. Soros is similarly tenuous. Its chairman, Mark Malloch-Brown, sits on the board of Mr. Soros’s Open Society Foundations and, Smartmatic notes, a dozen other organizations.