Abstract:
A technique of differentiation with respect to the distance to
the boundary of an outer parallel-body is applied to known measures of
sets of p-dimensional linear spaces which intersect a general convex
body in n-dimensional euclidean space in order to obtain an appropriate
definition of the measures of sets of p-dimensional linear spaces which
are tangent to a general convex body in n-space. A few side results
are obtained along the way, and there are included two applications of
these measures of tangents. The first is a simple application to geometric
probabilities in 3-space, and the second yields a new and
integro-geometric proof of Kubota's formula.
