The total absolute curvature of an equiaffine immersion

For an equiaffine immersion of general codimension, we recently defined the Lipschitz-Killing curvature, where we fix a transversal bundle and a transversal volume element. The main purpose of this paper is to show that the integration of the absolute value of the Lipschitz-Killing curvature is independent of the choices of a transversal bundle and a transversal volume element.