The integro-geometric tangent measures of euclidean n-space Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/sf268797n

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  • 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.
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