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测度论

版次：1
页数：
字数：
印刷时间：2009年06月01日
开本：16开
纸张：胶版纸
包装：平装
是否套装：否
国际标准书号ISBN：9787510004780

作者:（美）杜波　著出版社:世界图书出版公司出版时间:2009年06月

内容简介

本书是Springer研究生数学丛书之一，对测度论的讲述完全不同于一般的教程。该书将概率论作为测度论的必不缺少的一部分，所以书中的许多例子都是来自概率论，如独立性、马尔科夫过程、条件期望这些都作为本书的组成部分而不是将其置于附录中作为补充。特别是对Sigma代数做了较多的研究，而不是拿来即用。运用伪度量而不是度量给出了集合空间和函数空间的距离更直观的定义。

目　　录

Introduction
O. Conventions and Notation
1.Notation: Euclidean space
2.Operations involving
3.Inequalities and inclusions
4.A space and its subsets
5.Notation: generation of classes of sets
6.Product sets
7.Dot notation for an index set
8.Notation: sets defined by conditions on functions
9.Notation: open and closed sets
10.Limit of a function at a point
11.Metric spaces
12.Standard metric space theorems

Introduction O. Conventions and Notation 1.Notation: Euclidean space 2.Operations involving 3.Inequalities and inclusions 4.A space and its subsets 5.Notation: generation of classes of sets 6.Product sets 7.Dot notation for an index set 8.Notation: sets defined by conditions on functions 9.Notation: open and closed sets 10.Limit of a function at a point 11.Metric spaces 12.Standard metric space theorems 13.Pseudometric spaces I. Operations on Sets I.Unions and intersections 2.The symmetric difference operator 3.Limit operations on set sequences 4.Probabilistic interpretation of sets and operations on them II. Classes of Subsets of a Space 1.Set algebras 2.Examples 3.The generation of set algebras 4.The Borel sets of a metric space 5.Products of set algebras 6.Monotone classes of sets III. Set Functions 1.Set function definitions 2.Extension of a finitely additive set function 3.Products of set functions 4.Heuristics on a algebras and integration 5.Measures and integrals on a countable space 6.Independence and conditional probability (preliminary discussion) 7.Dependence examples 8.Inferior and superior limits of sequences of measurable sets 9.Mathematical counterparts of coin tossing 10.Setwise convergence of measure sequences 11.Outer measure 12.Outer measures of countable subsets of R 13.Distance on a set algebra defined by a subadditive set function 14.The pseudometric space defined by an outer measure 15.Nonadditive set functions IV. Measure Spaces 1.Completion of a measure space (S,$,~,) 2.Generalization of length on R 3.A general extension problem 4.Extension of a measure defined on a set algebra 5.Application to Borel measures 6.Strengthening of Theorem 5 when the metric space S is complete and separable 7.Continuity properties of monotone functions 8.The correspondence between monotone increasing functions on R and measures on B(R) 9.Discrete and continuous distributions on R 10.Lebesgue-Stieltjes measures on R/v and their corresponding monotone functions 11.Product measures 12.Examples of measures on RN 13.Marginal measures 14.Coin tossing 15.The Caratheodory measurability criterion 16.Measure hulls V. Measurable Functions 1.Function measurability 2.Function measurability properties 3.Measurability and sequential convergence 4.Baire functions 5.Joint distributions 6.Measures on function (coordinate) space …… VI. Intezration VII. Hilbert Soace VIII. Convergence of Measure Sequences IX. Signed Measures X. Measures and Functions of Bounded Variation on R XI. Conditional Expectations; Martingale Theory Notation Index

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