測度論(第2版英文) ,

作者:D·L·科恩

出版社:世界圖書出版公司北京公司

ISBN:9787519224134

$33.25

產品號碼: 85748 貨號: 9787519224134 分類: , 標籤: , ,

《測度論》是一部為初學者提供學習測度論的入門書籍,綜合性強,清晰易懂。本版與第1版相比,篇幅擴展100頁,並新增概率一章。全面介紹了測度和積分,重在強調學習分析和測度必需的和相關的一些話題。前五章講述了抽象測度和積分;第六章講述微分知識,包括Rd上變數的處理。每章末附有代表性的習題,從常規題型到擴展訓練都有涉及,較高難度的習題附有提示。

目錄

Introduction

1 Measures
1.1 Algebras and Sigma-Algebras
1.2 Measures
1.3 Outer Measures
1.4 Lebesgue Measure
1.5 Completeness 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, Complex-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 Complex Measures
4.1 Signed and Complex 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 Fubini's 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 Compact Spaces
7.1 Locally Compact Spaces
7.2 The Riesz Representation Theorem
7.3 Signed and Complex Measures; Duality
7.4 Additional Properties of Regular Measures
7.5 The μ*-Measurable Sets and the Dual ofL1
7.6 Products of Locally Compact 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

作者介紹

D.L.Cohn是美國Suffolk大學教授,本書的最大特點是初步並且全面的講述局部緊Hausdorff空間上的積分知識、Polish空間上的解析和Borel子集和局部緊群上的Haar測度,提供了調和分析和概率論的工具。

出版日期

07/01/2017

語系

簡體中文

版別

初版

裝訂

平裝

頁數

457

印刷

單色印刷

出版地

大陸