What is the ruling when the ball bounces into fair territory after being touched by a defensive player and then by the umpire?

When a ball that has been touched by a defensive player subsequently touches an umpire and then bounces into fair territory, the ruling is that the ball remains live. According to baseball rules, when a ball is in play and touches a player or an official, it does not automatically become dead unless it is clear that the ball is in a dead state due to other factors. In this situation, the key elements are that the ball was first touched by a defensive player, making it live, and then touched by the umpire without any action on the field that would indicate a dead ball situation. Therefore, since the ball continued to be in flight after these interactions, it stays live, allowing play to continue and the batter or other players to act upon it as normal.