测度论引论 (英文版)txt,chm,pdf,epub,mobi下载 作者: 陶哲轩 (Terence Tao) 出版社: 高等教育出版社 原作名: An Introduction to Measure theory 出版年: 2017-1 页数: 206 定价: 99.00 装帧: 精装 ISBN: 9787040469059 内容简介 · · · · · ·这是一本介绍测度论和积分理论基础的研究生教材,这些理论是现代实分析的基础。在转向抽象的测度和积分理论之前,《测度论引论(英文版)》先将注意力集中在Lebesgue测度和Lebesgue积分的具体构架上(它们由更经典的Jordan测度和Riemann积分所启发),内容包括标准收敛定理、Fubini定理以及Caratheodory延拓定理。由于与概率论有关,《测度论引论(英文版)》还包含一些经典的微分定理,例如Lebesgue和Rademacher微分定理。《测度论引论(英文版)》覆盖了一年级研究生实分析课程一季度或一学期的内容。 《测度论引论(英文版)》强调将学科的抽象和具体方面结合起来,用后者去解释和启发前者。一些主要原理(如Littlewood的三原理)提供了对学科的宣觉能力,这种关键作用也在书中得以强调。全书通篇包含大量习题,它们发展了理论的重要... 作者简介 · · · · · ·Terence Tao was the winner of the 2014 Breakthrough Prize in Mathematics. He is the James and Carol Collins Chair of mathematics at UCLA and the youngest person ever to be promoted to full professor at the age of 24. In 2006 Tao became the youngest ever mathematician to win the Fields Medal. His other honours include the George Polya Prize from the Society for Industrial and Ap... 目录 · · · · · ·PrefaceNotation Acknowledgments Chapter 1.Measure theory 1.1.Prologue:The problem of measure 1.2.Lebesgue measure · · · · · · () Preface Notation Acknowledgments Chapter 1.Measure theory 1.1.Prologue:The problem of measure 1.2.Lebesgue measure 1.3.The Lebesgue integral 1.4.Abstract measure spaces 1.5.Modes of convergence 1.6.Differentiation theorems 1.7.Outer measures,pre—measures, and product measures Chapter 2.Related articles 2.1.Problem solving strategies 2.2.The Rademacher differentiation theorem 2.3.Probability spaces 2.4.Infinite product spaces and the Kolmogorov extension theorem Bibliography Index · · · · · · () |
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