Translative and kinematic integral formulae for support functions

In continuation of earlier investigations in translative integral geometry, a translative formula is proved for support functions of convex bodies. As consequences, a kinematic formula for support functions is obtained, as well as a new interpretation of the mean section body, introduced in Goodey and Weil (Math. Proc. Camb. Phil. Soc. 112, (1992), 419–430).