测度论(第2版影印版)(英文版) 文教科普读物 (美)d.l.科恩
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作者(美)d.l.科恩
出版社世界图书出版公司
ISBN9787519224134
出版时间2017-07
版次1
装帧平装
开本16
页数457页
定价99元
货号521_9787519224134
上书时间2024-07-03
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目录：
introduction
1 measures
1.1 algebras and sigma-algebras
1.2 measures
1.3 outer measures
1.4 lebesgue measure
1.5 pleteness and regularity
1.6 dynkin classes
2 functions and integrals
2.1 measurable functions
2.2 properties that hold almost everywhere
2.3 the integral
2.4 limit theorems
2.5 the riemann integral
2.6 measurable functions again， plex-valued functions， and image measures
3 convergence
3.1 modes of convergence
3.2 normed spaces
3.3 definition of lp and lp
3.4 properties of lp and lp
3.5 dual spaces
4 signed and plex measures
4.1 signed and plex measures
4.2 absolute continuity
4.3 singularity
4.4 functions of finite variation
4.5 the duals of the lp spaces
5 product measures
5.1 constructions
5.2 fubinis theorem
5.3 applications
6 differentiation
6.1 change of variable in rd
6.2 differentiation of measures
6.3 differentiation of functions
7 measures on locally pact spaces
7.1 locally pact spaces
7.2 the riesz representation theorem
7.3 signed and plex measures； duality
7.4 additional properties of regular measures
7.5 the ?*-measurable sets and the dual ofl1
7.6 products of locally pact spaces
7.7 the daniell-stone integral
8 polish spaces and analytic sets
8.1 polish spaces
8.2 analytic sets
8.3 the separation theorem and its consequences
8.4 the measurability of analytic sets
8.5 cross sections
8.6 standard， analytic， lusin， and souslin spaces
9 haar measure
9.1 topological grou
9.2 the estence and uniqueness of haar measure
9.3 properties of haar measure
9.4 the algebras l1 （g） and m（g）
10 probability
10.1 basics
10.2 laws of large numbers
10.3 convergence in distribution and the central limit theorem
10.4 conditional distributions and martingales
10.5 brownian motion
10.6 construction of probability measures
anotation and set theory
balgebra and basic facts about r and c
ccalculus and topology in rd
dtopological spaces and metric spaces
ethe bochner integral
fliftings
gthe banach-tarski paradox
hthe henstock-kurzweii and mcshane integrals
references
index of notation
index
内容简介：
测度论（第2版 影印版 英文版）是一部为初学者提供学测度论的入门书籍，综合强，清晰易懂。本版与版相比，篇幅扩展100页，并新增概率一章。测度论（第2版 影印版 英文版）全面介绍了测度和积分，重在强调学分析和测度必需的和相关的一些话题。前几章讲述了抽象测度和积分；后一章讲述微分知识，包括rd上变量的处理。每章末附有代表的题，从常规题型到扩展训练都有涉及，较高难度的题附有提示。
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