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实分析教程-第2版-(影印版)

2020-06-21 00:00:00

实分析教程-第2版-(影印版) 内容简介《实分析教程(第2版)》编著者麦克唐纳。《实分析教程》是一部备受专家好评的教科书，书中用现代的方式清晰论述了实分析的概念与理论，定理证明简明易懂，可读性强，全书共有200道例题和1200例习题。《实分析教程》的写法像一部文学读物，这在数学教科书很少见，因此阅读本书会是一种享受。实分析教程-第2版-(影印版) 目录 preface part one set theory，real numbers，and calculus 1 set theory biography: georg cantor 1.1 basic definitions and properties 1.2 functions and sets 1.3 equivalence of sets； countability 1.4 algebras，σ-algebras，and monotone classes 2 the real number system and calculus biography: georg friedrich bernhard riemann 2.1 the real number system 2.2 sequences of real numbers 2.3 open and closed sets 2.4 real-valued functions 2.5 the cantor set and cantor function 2.6 the riemann integral part two measure，integration，and differentiation 3 lebesgue theory on the real line biography: emile felix-edouard-justin borel 3.1 borel measurable functions and borel sets 3.2 lebesgue outer measure 3.3 further properties of lebesgue outer measure 3.4 lebesgue measure 4 the lebesgue integral on the real line biography: henri leon lebesgue 4.1 the lebesgue integral for nonnegative functions 4.2 convergence properties of the lebesgue integral for nonnegative functions 4.3 the general lebesgue integral 4.4 lebesgue almost everywhere 5 elements of measure theory biography: constantin carath~odory 5.1 measure spaces 5.2 measurable functions 5.3 the abstract lebesgue integral for nonnegative functior 5.4 the general abstract lebesgue integral 5.5 convergence in measure 6 extensions to measures and product measure biography: guido fubini 6.1 extensions to measures 6.2 the lebesgue-stieltjes integral 6.3 product measure spaces 6.4 iteration of integrals in product measure spaces 7 elements of probability biography: andrei nikolaevich kolmogorov 7.1 the mathematical model for probability 7.2 random variables 7.3 expectation of random variables 7.4 the law of large numbers 8 differentiation and absolute continuity biography: giuseppe vitafi 8.1 derivatives and dini-derivates 8.2 functions of bounded variation 8.3 the indefinite lebesgne integral 8.4 absolutely continuous functions 9 signed and complex measures biography: johann radon 9.1 signed measures 9.2 the radon-nikodym theorem 9.3 signed and complex measures 9.4 decomposition of measures 9.5 measurable transformati6ns and the general change-of-variable formula part three topological, metric, and normed spaces 10 topologies, metrics, and norms biography: felix hausdorff 10.1 introduction to topological spaces 10.2 metrics and norms 10.3 weak topologies 10.4 closed sets, convergence, and completeness 10.5 nets and continuity 10.5 separation properties 10.7 connected sets 11 separability and compactness biography: maurice frechet 11.1 separability, second countability, andmetrizability 11.2 compact metric spaces 11.3 compact topological spaces 11.4 locally compact spaces 11.5 function spaces 12 complete and compact spaces biography: marshall harvey stone 12.1 the baire category theorem 12.2 contractions of complete metric spaces 12.3 compactness in the space c(□, a) 12.4 compactness of product spaces 12.5 approximation by functions from a lattice 12.5 approximation by functions from an algebra 13 hilbert spaces and banach spaces biography: david hilbert 13.1 preliminaries on normed spaces 13.2 hilbert spaces 13.3 bases and duality in hilbert spaces 13.4 □-spaces 13.5 nonnegative linear functionals on c(□) 13.5 the dual spaces of c(□) and c0(□) 14 normed spaces and locally convex spaces biography: stefan banach 14.1 the hahn-banach theorem 14.2 linear operators on banach spaces 14.3 compact self-adjoint operators 14.4 topological linear spaces 14.5 weak and weak* topologies 14.5 compact convex sets part four harmonic analysis, dynamical systems, and hausdorff measure 15 elements of harmonic analysis biography: ingrid daubechies 15.1 introduction to fourier series 15.2 convergence of fourier series 15.3 the fourier transform 15.4 fourier transforms of measures 15.5 □-theory of the fourier transform 15.5 introduction to wavelets 15.7 orthonormal wavelet bases; the wavelet transform 15 measurable dynamical systems biography: claude e/woodshannon 16.1 introduction and examples 16.2 ergodic theory 16.3 isomorphism of measurable dynamical systems;entropy 16.4 the kolmogorov-sinai theorem; calculation of entropy 17 hausdorff measure and fractals biography: benoit b.mandelbrot 17.1 outer measure and measurability 17.2 hausdorff measure 17.3 hausdorff dimension and topological dimension 17.4 fractals index

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实分析教程-第2版-(影印版) 内容简介

实分析教程-第2版-(影印版) 目录