Measure Theory and Fine Properties of Functions (Hardcover)

GENERAL MEASURE THEORY
Measures and Measurable Functions
Lusin's and Egoroff's Theorems
Integrals and Limit Theorems
Product Measures, Fubini's Theorem, Lebesgue Measure
Covering Theorems
Differentiation of Radon Measures
Lebesgue Points
Approximate continuity
Riesz Representation Theorem
Weak Convergence and Compactness for Radon Measures

HAUSDORFF MEASURE
Definitions and Elementary Properties; Hausdorff Dimension
Isodiametric Inequality
Densities
Hausdorff Measure and Elementary Properties of Functions

AREA AND COAREA FORMULAS
Lipschitz Functions, Rademacher's Theorem
Linear Maps and Jacobians
The Area Formula
The Coarea Formula

SOBOLEV FUNCTIONS.
Definitions And Elementary Properties. Approximation
Traces. Extensions. Sobolev Inequalities
Compactness. Capacity
Quasicontinuity; Precise Representations of Sobolev Functions. Differentiability on Lines

BV FUNCTIONS AND SETS OF FINITE PERIMETER
Definitions and Structure Theorem
Approximation and Compactness
Traces. Extensions. Coarea Formula for BV Functions. Isoperimetric Inequalities.
The Reduced Boundary
The Measure Theoretic Boundary; Gauss-Green Theorem. Pointwise Properties of BV Functions
Essential Variation on Lines
A Criterion for Finite Perimeter. DIFFERENTIABILITY AND APPROXIMATION BY C1 FUNCTIONS.
Lp Differentiability a.e.; Approximate Differentiability
Differentiability A.E. for W1,P (P > N). Convex Functions
Second Derivatives a.e. for convex functions
Whitney's Extension Theorem
Approximation by C1 Functions

NOTATION
REFERENCES