Athing Mu of the United States won the gold medal in the Olympic women’s 800 metres final on Tuesday, her country’s first victory in the event in more than half a century, as her compatriot Raevyn Rogers grabbed bronze. Keely Hodgkinson of Britain took silver. The absence of South Africa’s double champion Caster Semenya, ruled ineligible due to heightened testosterone levels, opened up the field to a new winner. Mu took full advantage as she dominated the race, leading almost from the start and crossing the line clear of her rivals in a time of 1:55.21.