ANALYSIS AND VALUATION OF CONVEX SETS

Abstract

This dissertation explores the valuation of convex sets in Euclidean space. Starting with the Steiner formula, which provides a basis for studying mixed volumes, it pro ceeds to prove Groemer‘s integral theorem, showing how valuations extend within convex sets. The final chapter focuses on Hadwiger‘s theorem and its applications to projections and Grassmannians, offering insights into intrinsic volumes and their geo metric significance. These findings contribute to a clearer understanding of valuation theory in convex geometry.