Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics.
Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics.
Preface Set Theory and General Topology Compactness and Continuous Functions Banach Spaces Hilbert Spaces Calculus in Banach Space Locally Convex Topological Vector Spaces Measures and Measurable Functions The Abstract Lebesgue Integral The Construction of Measures Lebesgue Measure Product Measure The Lp Spaces Representation Theorems Fundamental Theorem of Calculus General Radon Measures Fourier Transforms Probability Weak Derivatives Hausdorff Measures The Area Formula The Coarea Formula Fourier Analysis in Rn Integration for Vector Valued Functions Convex Functions Appendix 1: The Hausdorff Maximal Theorem Appendix 2: Stone's Theorem and Partitions of Unity Appendix 3: Taylor Series and Analytic Functions Appendix 4: The Brouwer Fixed Point Theorem References Index
Preface Set Theory and General Topology Compactness and Continuous Functions Banach Spaces Hilbert Spaces Calculus in Banach Space Locally Convex Topological Vector Spaces Measures and Measurable Functions The Abstract Lebesgue Integral The Construction of Measures Lebesgue Measure Product Measure The Lp Spaces Representation Theorems Fundamental Theorem of Calculus General Radon Measures Fourier Transforms Probability Weak Derivatives Hausdorff Measures The Area Formula The Coarea Formula Fourier Analysis in Rn Integration for Vector Valued Functions Convex Functions Appendix 1: The Hausdorff Maximal Theorem Appendix 2: Stone's Theorem and Partitions of Unity Appendix 3: Taylor Series and Analytic Functions Appendix 4: The Brouwer Fixed Point Theorem References Index
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