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。

]

目录

prefacepart one set theory，real numbers，and calculus1 set theorybiography: georg cantor1.1 basic definitions and properties1.2 functions and sets1.3 equivalence of sets； countability1.4 algebras，σ-algebras，and monotone classes2 the real number system and calculusbiography: georg friedrich bernhard riemann2.1 the real number system2.2 sequences of real numbers2.3 open and closed sets2.4 real-valued functions2.5 the cantor set and cantor function2.6 the riemann integralpart two measure，integration，and differentiation3 lebesgue theory on the real linebiography: emile felix-edouard-justin borel3.1 borel measurable functions and borel sets3.2  lebesgue outer measure3.3  further properties of lebesgue outer measure3.4 lebesgue measure4   the lebesgue integral on the real linebiography: henri leon lebesgue4.1  the lebesgue integral for nonnegative functions4.2  convergence properties of the lebesgue integral fornonnegative functions4.3  the general lebesgue integral4.4  lebesgue almost everywhere5 elements of measure theorybiography: constantin carath~odory5.1  measure spaces5.2 measurable functions5.3 the abstract lebesgue integral for nonnegative functior5.4 the general abstract lebesgue integral5.5  convergence in measure6 extensions to measures and product measurebiography: guido fubini6.1  extensions to measures6.2 the lebesgue-stieltjes integral6.3  product measure spaces6.4 iteration of integrals in product measure spaces7 elements of probabilitybiography: andrei nikolaevich kolmogorov7.1  the mathematical model for probability7.2  random variables7.3  expectation of random variables7.4  the law of large numbers8 differentiation and absolute continuitybiography: giuseppe vitafi8.1  derivatives and dini-derivates8.2  functions of bounded variation8.3  the indefinite lebesgne integral8.4 absolutely continuous functions9 signed and complex measuresbiography: johann radon9.1  signed measures9.2  the radon-nikodym theorem9.3  signed and complex measures9.4  decomposition of measures9.5  measurable transformati6ns and the generalchange-of-variable formulapart threetopological, metric, and normed spaces10 topologies, metrics, and normsbiography: felix hausdorff10.1  introduction to topological spaces10.2  metrics and norms10.3 weak topologies10.4  closed sets, convergence, and completeness10.5  nets and continuity10.5  separation properties10.7  connected sets11 separability and compactnessbiography: maurice frechet11.1  separability, second countability, andmetrizability11.2  compact metric spaces11.3  compact topological spaces11.4  locally compact spaces11.5  function spaces12 complete and compact spacesbiography: marshall harvey stone12.1  the baire category theorem12.2  contractions of complete metric spaces12.3 compactness in the space c(□, a)12.4 compactness of product spaces12.5  approximation by functions from a lattice12.5  approximation by functions from an algebra13 hilbert spaces and banach spacesbiography: david hilbert13.1  preliminaries on normed spaces13.2 hilbert spaces13.3 bases and duality in hilbert spaces13.4 □-spaces13.5 nonnegative linear functionals on c(□)13.5 the dual spaces of c(□) and c0(□)14 normed spaces and locally convex spacesbiography: stefan banach14.1  the hahn-banach theorem14.2  linear operators on banach spaces14.3 compact self-adjoint operators14.4 topological linear spaces14.5  weak and weak* topologies14.5  compact convex setspart fourharmonic analysis, dynamical systems, and hausdorff measure15 elements of harmonic analysisbiography: ingrid daubechies15.1 introduction to fourier series15.2  convergence of fourier series15.3  the fourier transform15.4 fourier transforms of measures15.5 □-theory of the fourier transform15.5  introduction to wavelets15.7  orthonormal wavelet bases; the wavelet transform15 measurable dynamical systems biography: claude e/woodshannon16.1  introduction and examples16.2 ergodic theory16.3  isomorphism of measurable dynamical systems;entropy16.4 the kolmogorov-sinai theorem; calculation of entropy17 hausdorff measure and fractals biography: benoit b.mandelbrot17.1  outer measure and measurability17.2  hausdorff measure17.3  hausdorff dimension and topological dimension17.4 fractalsindex

封面

书名:实分析教程-第2版-(影印版)

作者:（美）麦克唐纳 著

页数:667

定价:¥139.0

出版社:世界图书出版公司

出版日期:2013-01-01

ISBN:9787510052637

PDF电子书大小:36MB 高清扫描完整版