This popular textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.

Lawrence Craig Evans, University of California, Berkeley, USA

Ronald F. Gariepy, University of Kentucky, Lexington, USA

1 Measure Theory

2 Hausdorff Measures

3 Area and Coarea Formulas

4 Sobolev Functions

5 Functions of Bounded Variation, Sets of Finite Perimeter

6 Differentiability, Approximation by C1 Functions