Ball screw for a motor vehicle brake and motor vehicle brake

The ball screw (36) has a rotationally drivable spindle (38). A nut (40) is axially moved towards requirement of the rotationally drivable spindle relative to the ball screw. A rolling body arrangement (42) is arranged between the spindle and the nut, and is displaced in the ball screw. The rolling body arrangement is pre-stressed over a spring element in a pre-determined initial position. An independent claim is included for a motor vehicle brake, particularly electromechanically actuated with a brake pad displaced relative to a housing.