REAL ANALYSIS:THEORY OF MEASURE AND INTEGRATION (2ND EDITION)

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This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theor

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Harvard Library

Measure and Outer Measure; Regularity of Measures; Measurable Mappings; Completion of a Measure Space; Convergence Almost Everywhere; Almost Uniform Convergence; Convergence in Measure; Integration with Respect to a Measure; Generalized Convergence Theorems for Integrals; Signed Measures; Absolute Continuity of a Measure with Respect to Another; Monotone Functions and Functions of Bounded Variation on R; Absolutely Continuous Functions; Convex Functions, Differentiation of an Indefinite Integral; Banach Spaces; Lp Spaces for p in (0, ); Bounded Linear Functionals; Integration on a Locally Compact Hausdorff Space; Extension of Additive Set Functions to Measures; Lebesgue–Stieltjes Measure Space; Product Measure Spaces; Convolution of Functions; Integration with Respect to Lebesgue Measure on Euclidean Spaces; Integral and Linear Transformations of the Integral; Hardy–Littlewood Maximal Theorem; Lebesgue Differentiation Theorem; Change of Variable of Integration by Differentiable Transformations; Hausdorff Measures on Euclidean Spaces; Hausdorff Dimensions; Transformation of Hausdorff Measures.

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REAL ANALYSIS:THEORY OF MEASURE AND INTEGRATION (2ND EDITION) 实分析：测度与积分理论 第2版 数学分析

REAL ANALYSIS:THEORY OF MEASURE AND INTEGRATION (2ND EDITION)

实分析：测度与积分理论第2版
数学分析