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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

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