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When a man regarded as the deadliest sniper in U.S. history detailed his kills in a bestselling autobiography, he also included details about a 2006 incident in which he says he punched a guy he called "Scruff Face" — later identified as former Minnesota Gov. Jesse Ventura.

Ventura, a public figure with a tough-guy image, says the fight didn't happen, and he sued author Chris Kyle for defamation. The trial begins Tuesday, and it will be up to Ventura's attorneys to prove that Kyle's account about that night in a California bar was false — and even more difficult, that Kyle knew it.

"Ventura is going to have to prove falsity ... but the harder part is proving actual malice," said Raleigh Levine, a law professor at William Mitchell College of Law in St. Paul. "It has to do with what you know about the truth — that you actually knew that what you were saying was false or that you recklessly disregarded the truth."

Besides sorting out what happened in the bar, jurors will have to assess whether Ventura's reputation was damaged and whether Kyle used Ventura's name to make a profit.

Kyle and a friend were killed in February 2013 at a Texas gun range, allegedly by an Iraq War veteran they were trying to help. Kyle's widow, Taya Kyle, is now the defendant.

Big money may be at stake. Court documents show Kyle's book had earned royalties of more than $3 million as of June 30, 2013, and the judge already has ruled that proceeds from an upcoming movie could be subject to damages, too.

Ventura has said the case isn't about money. "It's about clearing my name. It's a lie," Ventura told The Associated Press in February.

Ventura and Taya Kyle are both expected to testify during the trial, which will likely last more than two weeks.

Ventura, a former Navy SEAL and pro wrestler whose post-political life has included hosting several cable TV shows, claims Kyle defamed him to gain notoriety for his best-selling 2012 book, "American Sniper," which describes his kills of insurgents from 1999 to 2009. A movie based on the book, starring Bradley Cooper, is in production.

In the book, Kyle describes an incident in which he claims Ventura was speaking loudly against President George W. Bush, the Iraq War and Navy SEAL tactics. Kyle, also a former Navy SEAL, claimed Ventura said the SEALS "deserve to lose a few." Kyle wrote that he punched Ventura, knocking him to the ground.

Ventura denies making those statements, and says Kyle never laid a hand on him. Kyle had maintained the events in the book are true, and the essence of what was said is accurate, court documents say.

Both sides have witnesses to back up their version of events; and attorneys have cast doubt on the opposing witnesses' credibility. While Kyle's book says "rumor has it" Ventura had a black eye the next day, photos of Ventura from that time don't show him with any visible injury, according to court documents.

In March, U.S. District Judge Richard Kyle — no relation to Chris or Taya Kyle — said the case could go forward because Ventura had offered sufficient evidence that could lead a jury to conclude Kyle's statements were false.

But because Ventura is a public figure, the judge wrote, Ventura must show "actual malice" or prove by clear and convincing evidence that Kyle knew the statements were false or acted in reckless disregard of the truth.

Levine said Ventura has a high bar to clear, and to win damages, he must also prove his reputation was harmed in a quantifiable way.

In a November deposition, Ventura said his job offers dried up after the book was published, and he was worried about being seen as a traitor to the military. He also said publicity Kyle got from interviews about the alleged incident with Ventura helped Kyle's book sales and led to the film option.

The defense argues in court documents that the public embraced Kyle's book for reasons "completely unrelated to any passing reference to Ventura," and that the book has been more successful than any Ventura has written.