If a batted ball hits an umpire in fair territory is the ball live?

According to MLB rules, that would depend on the situation. MLB Rule 5.09(f) states that the ball becomes dead and runners advance one base, or return to their bases, without liability to be put out when "A fair ball touches a runner or an umpire on fair territory before it touches an infielder including the pitcher, or touches an umpire before it has passed an infielder other than the pitcher. Rule 5.09(f) Comment: If a fair ball touches an umpire working in the infield after it has bounded past, or over, the pitcher, it is a dead ball. If a batted ball is deflected by a fielder in fair territory and hits a runner or an umpire while still in flight and then is caught by an infielder it shall not be a catch, but the ball shall remain in play." If the ball hits the umpire first, the ball is dead. If a defensive player touches the ball and then the ball hits the umpire, the ball is live.