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Washington DC: Washington DC police say four people have died during the storming of the Capitol building.
In addition to the woman shot by police, three others died as a result of "medical emergencies".
So far, more than 52 people have been arrested - 47 of them for curfew violations.
US media are reporting the woman shot and killed during the storming of the Capitol was San Diego resident Ashli Babbitt. A US Air Force veteran, she is thought to have been shot after entering the building alongside other rioters.
US broadcaster Fox5 spoke to the woman's mother-in-law who said Babbitt had been a Trump supporter.
She is thought to have been shot at around 15:00 Washington time, and was rushed to hospital but later pronounced dead.