Measure Theory and Fine Properties of Functions, Revised Edition 1st Edition

Description

This book emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems and differentiation in Rn , Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. This second edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the p- theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.