Reality Check: Third Clinton v Trump presidential debate

Here are some of the statements made by Hillary Clinton and Donald Trump in their third and final presidential debate and how they compare with the facts.

Claim: Donald Trump says the violence at some of his rallies, including one in Chicago, was caused by the Clinton campaign and President Obama.

Reality Check verdict: This relates to videos released by right wing blogger James O'Keefe's Project Veritas. Hidden camera footage appears to show executives working for companies helping the Clinton campaign and the Democratic National Committee talking about training volunteers to attend Trump rallies and incite violence.

One of them, Scott Foval, is heard saying it did not take much to provoke Trump supporters because they are "naturally psychotic". Others are shown apparently boasting about provoking violence outside a Trump rally in Chicago.

Foval was fired as National Field Director for Clinton-supporting PAC Americans United for Change on Monday over the videos.

Robert Creamer, another Democrat contractor caught in the undercover sting, has "stepped back" from the Clinton campaign over the "dirty tricks" allegations, despite claiming the "hypothetical conversations" recorded for the video never took place.

The Clinton campaign has denied planting protesters and deliberately inciting violence at rallies - and highlighted criticism of O'Keefe's previous undercover stings, which have been accused of using selective editing.

"While Project Veritas has been known to offer misleading video out of context, some of the language and tactics referenced in the video are troubling even as a theory or proposal never executed," Zac Petkanas, a spokesman for Clinton's campaign, said in a statement.

"We support the Democratic National Committee's appropriate action addressing this matter and look forward to continue waging a campaign of ideas worthy of our democratic process."

But Trump supporter Jeffrey Lord told CNN the American left had a history of this kind of behaviour and it was "totally unacceptable".

Claim: Trump has repeatedly claimed that Russian President Vladimir Putin has praised him.

Reality Check verdict: This does not appear to be true. In 2015, Putin used the Russian word Yarkii to describe the Republican nominee, which Russian language experts translate as " a lively personality".

Putin, himself, denied the "brilliant" translation in a June interview with CNN.

"You made some comments about the American Republican presumptive nominee Donald Trump. You called him 'brilliant,' 'outstanding,' 'talented,' " CNN's Fareed Zakaria said.

"These comments were reported around the world. I was wondering what in him led you to that judgment and do you still hold that judgment?"

"Why do you always change the meaning of what I said?" Putin responded through an interpreter.

"I only said that he was a 'bright person.' Isn't he bright? He is. I did not say anything else about him."

Claim: Hillary Clinton justifies her call for gun control by saying that in America there are 33,000 gun deaths a year.

Reality Check verdict: Clinton's figure comes from the Centre for Disease Control and Prevention's Multiple Cause of Death database. The figure is for 2014, the most recent available. To put it in context, 33% of those deaths were homicides; 63% were suicides.

Claim: Donald Trump has repeatedly used Chicago as an example of a city where violence is out of control.

Reality Check verdict: Chicago's homicide rate is far higher than other big cities such as New York and Los Angeles. So far this year more than 600 people have been killed, a 24% increase on the same period last year. Non-fatal shootings are also up. But analysis of FBI data by CNN suggests it is not the homicide capital of the US. New Orleans, St Louis, Detroit, Baltimore and Newark all have higher per capita homicide rates.

Claim: Trump has been claiming for days that the electoral system is rigged and riddled with corruption - and that voter fraud is "very common".

Reality Check verdict: Trump is quoting from a 2012 study by non-partisan research organisation Pew, which found approximately 24 million - or one of every eight - US voter registrations were no longer valid or were significantly inaccurate. Of those, the report says, 1.8 million were deceased.

But the Pew report did not say the 1.8 million deceased people actually voted. It said the discrepancies were evidence of a need to upgrade systems of voter registration.

Other researchers say voter fraud involving ballots - including votes cast by dead people - is rare.

In a comprehensive study of the subject, Justin Levitt, a professor at Loyola Law School, found 31 credible incidents out of more than 1 billion votes cast from 2000 to 2014.

Is the US election really rigged?

Claim: Donald Trump's economic plans would give massive tax cuts to the well-off, bigger than any previous president.

Reality Check verdict: George W Bush cut the top rate of income tax from 39.6% to 35%.

Under Trump's plan, seven tax brackets would be collapsed into four, cutting the top rate from 39.6% to 33%.

According to the right-leaning Tax Foundation, Trump's plan would increase after-tax incomes of the wealthy by between 10.2% to 19.9%. According to the left-leaning Centre on Budget and Policy Priorities the Bush tax cuts increased the after-tax income of the top 1% of earners between 5.3% and 6.7% from 2004 to 2012.

Going further back there were presidents who gave bigger tax cuts to the highest earners, although the top rate was set at a far higher level than it is today.

John F Kennedy wanted to reduce the top rate from 91% to 65%. His successor Lyndon Johnson succeeded in getting a cut of 91% to 70% as part of a broader package of tax reductions.

Ronald Reagan cut the top rate from 70% to 50% in 1981 and then, in 1986, he reduced it further to 28%.

Claim: Trump attacks Clinton's record in office, telling her: "When you ran the state department, $6bn was missing! Maybe it was stolen… nobody knows."

Reality Check verdict: It's a claim Trump has made before - and a claim that has been debunked before. It relates to a management alert issued in March 2014 by the State Department's Inspector General Steve Linick, obtained under freedom of information laws.

The alert highlighted paperwork deficiencies in closing out contracts issued in Iraq, Afghanistan and Africa.

Mr Linick hit back at media reporting of the $6bn figure in a 13 April letter to the Washington Post on 13 April saying it was wrong to assume $6bn was "missing".

The alert, he wrote, "did not draw that conclusion". Instead, he wrote, the point of the alert was "the failure to adequately maintain contract files - documents necessary to ensure the full accounting of US tax dollars - 'creates significant financial risk and demonstrates a lack of internal control over the Department's contract actions.'"

In other words, it was paperwork, rather than cash, that was missing.

Claim: Donald Trump suggests Hillary Clinton supports full-term abortion, claiming that it can take place just two or three days before birth.

Reality Check verdict: This is probably a reference to comments made by Clinton during the Democratic primaries, when she said late-term abortions "are because of medical necessity".

She told Trump during the debate: "That is not what happens in these cases." And she is right - late-term abortions of the kind spoken about so graphically by Trump are very rare.

Data from the Guttmacher institute show most abortions take place early in pregnancy. Only 1.2% of abortions in the US - about 12,000 a year - take place after 21 weeks.

Some 43 states already prohibit some abortions after a certain point in pregnancy - so full-term abortion is banned in much of the country. There is no definitive information as to how many of those abortions are due to medical necessity.