AMNA NAWAZ: And now to a closer look at a momentous week in politics.

GEOFF BENNETT: First to the Republicans, who capped off their national convention in Milwaukee last night with a speech from the man who has reshaped the party in his own image.

That's former President Donald Trump.

Lisa Desjardins has this report.

LISA DESJARDINS: Balloons rained down from the rafters, and Donald Trump rained from on stage, as Republicans cheered his third presidential nomination.

He is just the sixth American to achieve that for a major party, but the event marking it was all on his brand, an unapologetic show... HULK HOGAN, Former Professional Wrestler: Enough was enough.

(CHEERING) HULK HOGAN: And I said, let Trumpamania run wild, brother.

Let Trumpamania rule again.

Let Trumpamania make America great again.

LISA DESJARDINS: With a get-tough theme from wrestler Hulk Hogan, singer Kid Rock, and Ultimate Fighting Championship CEO Dana White.

DANA WHITE, President, Ultimate Fighting Championship: I'm in the tough guy business.

And this man is the toughest, most resilient human being that I have ever met in my life!

(APPLAUSE) (CHEERING) LISA DESJARDINS: And when Trump arrived on stage, the music shifted tone, but the message, literally his name, was still big.

To a captivated crowd, the Florida Republican initially made good on the promise of a unifying tone.

DONALD TRUMP, Former President of the United States (R) and Current U.S. Presidential Candidate: As Americans, we are bound together by a single fate and a shared destiny.

We rise together or we fall apart.

LISA DESJARDINS: He shared the story of surviving last weekend's assassination attempt.

DONALD TRUMP: The amazing thing is that prior to the shot, if I had not moved my head at that very last instant, the assassin's bullet would have perfectly hit its mark, and I would not be here tonight.

LISA DESJARDINS: But after that, the tone and rhetoric shifted, as Trump, staying on brand, repeatedly went off-script, repeating some stump speech claims that Republicans love, but which don't hold up.

DONALD TRUMP: Years ago under, my presidency, we had the most secure border and best economy in the history of our country and the history of the world.

We had no inflation, soaring incomes.

LOUIS JACOBSON, PolitiFact: So we call that false.

LISA DESJARDINS: We spoke to Lou Jacobson of PolitiFact.

LOUIS JACOBSON: But for all the standard metrics, things like the unemployment rate, things like wages, wage growth, GDP, these - - the first three years of Trump's tenure were not somehow the greatest in the U.S. history.

We can find examples of better economies in the '60s, for instance, much less the entire world.

LISA DESJARDINS: Another example: DONALD TRUMP: Bad things are going to happen.

Meanwhile, our crime rate is going up, while crime statistics all over the world are going down.

LOUIS JACOBSON: That is mostly false.

So, violent crimes, the things that people really care probably the most about, have been consistently going down under Biden.

In terms of property crimes, at least some kinds of property crimes, particularly motor vehicle thefts, those actually are up.

So there's a grain of truth there.

But for the most part, most types of crime, despite all that you hear on TV and from Trump himself, actually, if you look at the total number and the percentage, it's been going down for several years in a row.

LISA DESJARDINS: As for Trump's own criminal history, 34 felony convictions for falsifying business records, that wasn't mentioned directly, though he did rail against the justice system, implying his convictions by a New York jury were political.

DONALD TRUMP: The Democrat Party should immediately stop weaponizing the justice system and labeling their political opponent as an enemy of democracy.

LISA DESJARDINS: The 92-minute acceptance speech was the longest in modern political history, but it was not the only speech of note last night.

Earlier, Trump's son Eric raised culture notes, railing against the changing of Confederate base names, defending his father, and putting his doubters on notice.

ERIC TRUMP, Executive Vice President, Trump Organization: To all Americans watching tonight, the greatest retribution will be our success.

LISA DESJARDINS: Former news anchor turned podcaster Tucker Carlson brought conservative celebrity and full-throated praise of Trump.

TUCKER CARLSON, Former FOX News Anchor: I have been to many conventions.

I have never been to a more fun convention.

LISA DESJARDINS: But one of the most important figures made her impression without saying anything at all.

Melania Trump, absent until last night, walked into the convention floor to loud and warm applause.

The GOP Convention threaded many unusual needles like that, ending with a Trump family gathering on stage, aiming to show a unified and organized front, including with vice presidential nominee, J.D.

Vance.

He and Trump have their first joint campaign rally tomorrow, just across Lake Michigan in Grand Rapids.

For the PBS "News Hour," I'm Lisa Desjardins in Milwaukee.