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美 H L Royden 著
店铺: 互动创新图书专营店 出版社: 机械工业出版社 ISBN:7111139127 商品编码:27162985070 丛书名: 经典原版书库 出版时间:2004-03-01 页数:444
包邮 实分析(英文版 第3版)|17744 电子书 下载 mobi epub pdf txt
包邮 实分析(英文版 第3版)|17744-so88
包邮 实分析(英文版 第3版)|17744 pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
美 H L Royden 著
店铺: 互动创新图书专营店 出版社: 机械工业出版社 ISBN:7111139127 商品编码:27162985070 丛书名: 经典原版书库 出版时间:2004-03-01 页数:444
书名: | 实分析(英文版·第3版)|17744 |
图书定价: | 45元 |
图书作者: | (美)H.L.Royden |
出版社: | 机械工业出版社 |
出版日期: | 2004/3/1 0:00:00 |
ISBN号: | 7111139127 |
开本: | 16开 |
页数: | 444 |
版次: | 3-1 |
内容简介 |
本书为数学与统计学专业研究生实分析课程的基础教材,1963年出版了第1版,1987年修订的第3版在前两版的基础上进行了改写和补充,增加了可变测度一章。在过去的40多年中,本书已被国外众多著名大学(如斯坦福大学、哈佛大学等)采用。 本书是一本优秀的教材,主要分三部分:第一部分为实变函数论,第二部分为抽象空间,第三部分为一般测度与积分论。书中不仅包含数学定理和定义,而且还提出了挑战性的问题,以便读者更深入地理解书中内容。本书的题材是数学教学的共同基础,包含许多数学家的研究成果。 |
目录 |
Prologue to the Student 1 I Set Theory 6 1 Introduction 6 2 Functions 9 3 Unions, intersections, and complements 12 4 Algebras of sets 17 5 The axiom of choice and infinite direct products 19 6 Countable sets 20 7 Relations and equivalences 23 8 Partial orderings and the maximal principle 24 9 Well ordering and the countable ordinals 26 Part One THEORY OF FUNCTIONS OF A REAL VARIABLE 2 The Real Number System 31 1 Axioms for the real numbers 31 2 The natural and rational numbers as subsets of R 34 3 The extended real numbers 36 4 Sequences of real numbers 37 5 Open and closed sets of real numbers 40 6 Continuous functions 47 7 Borel sets 52 3 Lebesgue Measure 54 I Introduction 54 2 Outer measure 56 3 Measurable sets and Lebesgue measure 58 *4 A nonmeasurable set 64 5 Measurable functions 66 6 Littlewood's three principles 72 4 The Lebesgue Integral 75 1 The Riemann integral 75 2 The Lebesgue integral of a bounded function over a set of finite measure 77 3 The integral of a nonnegative function 85 4 The general Lebesgue integral 89 *5 Convergence in measure 95 S Differentiation and Integration 97 1 Differentiation of monotone functions 97 2 Functions of bounded variation 102 3 Differentiation of an integral 104 4 Absolute continuity 108 5 Convex functions 113 6 The Classical Banach Spaces 118 1 The Lp spaces 118 2 The Minkowski and Holder inequalities 119 3 Convergence and completeness 123 4 Approximation in Lp 127 5 Bounded linear functionals on the Lp spaces 130 Part Two ABSTRACT SPACES 7 Metric Spaces 139 1 Introduction 139 2 Open and closed sets 141 3 Continuous functions and homeomorphisms 144 4 Convergence and completeness 146 5 Uniform continuity and uniformity 148 6 Subspaces 151 7 Compact metric spaces 152 8 Baire category 158 9 Absolute Gs 164 10 The Ascoli-Arzela Theorem 167 8 Topological Spaces ltl I Fundamental notions 171 2 Bases and countability 175 3 The separation axioms and continuous real-valued functions 178 4 Connectedness 182 5 Products and direct unions of topological spaces 184 *6 Topological and uniform properties 187 *7 Nets 188 9 Compact and Locally Compact Spaces 190 I Compact spaces 190 2 Countable compactness and the Bolzano-Weierstrass property 193 3 Products of compact spaces 196 4 Locally compact spaces 199 5 a-compact spaces 203 *6 Paracompact spaces 204 7 Manifolds 206 *8 The Stone-Cech compactification 209 9 The Stone-Weierstrass Theorem 210 10 Banach Spaces 217 I Introduction 217 2 Linear operators 220 3 Linear functionals and the Hahn-Banach Theorem 222 4 The Closed Graph Theorem 224 5 Topological vector spaces 233 6 Weak topologies 236 7 Convexity 239 8 Hilbert space 245 Part Three GENERAL MEASURE AND INTEGRATION THEORY 11 Measure and Integration 253 1 Measure spaces 253 2 Measurable functions 259 3 Integration 263 4 General Convergence Theorems 268 5 Signed measures 270 6 The Radon-Nikodym Theorem 276 7 The Lp-spaces 282 12 Measure and Outer Measure 288 1 Outer measure and measurability 288 2 The Extension Theorem 291 3 The Lebesgue-Stieltjes integral 299 4 Product measures 303 5 Integral operators 313 *6 Inner measure 317 *7 Extension by sets of measure zero 325 8 Caratheodory outer measure 326 9 Hausdorff measure 329 13 Measure and Topology 331 1 Baire sets and Borel sets 331 2 The regularity of Baire and Borel measures 337 3 The construction of Borel measures 345 4 Positive linear functionals and Borel measures 352 5 Bounded linear functionals on C(X) 355 14 Invariant Measures 361 1 Homogeneous spaces 361 2 Topological equicontinuity 362 3 The existence ofinvariant measures 365 4 Topological groups 370 5 Group actions and quotient spaces 376 6 Unicity ofinvariant measures 378 7 Groups ofdiffeomorphisms 388 15 Mappings of Measure Spaces 392 1 Point mappings and set mappings 392 2 Boolean algebras 394 3 Measure algebras 398 4 Borel equivalences 401 5 Borel measures on complete separable metric spaces 406 6 Set mappings and point mappings on complete separable metric spaces 412 7 The isometries of Lp 415 16 The Daniell Integral 419 1 Introduction 419 2 The Extension Theorem 422 3 Uniqueness 427 4 Measurability and measure 429 Bibliography 435 Index of Symbols 437 Subject Index 439 |
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