实分析（英文版·第3版）
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| 新书城图书编号：947 |
| 图书ISBN：7111139127 |
| 出版时间：2004-3-2 |
| 出版社：机械工业出版社 |
| 作者：（美）罗伊登 著 |
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市场价格：￥45 |
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普通会员：￥36
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80折 |
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VIP会员：￥33.75
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75折 |
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【图书简介】
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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我年中，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的内容。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。
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【图书目录】
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Prologue to the Student
1 Set Theory
1 Introduction
2 Functions
3 Unions,intersections,and complements
4 Algebras of sets
5 The axiom of choice and infinite direct products
6 Countable sets
7 Relations and equivalences
8 Partial orderings and the maximal principle
9 Well ordering and the countable ordinals
Part One
THEORY OF FUNCTIONS OF A REAL VARIABLE
2 The Real Number System
1 Axioms for the real numbers
2 The natural and rational numbers as subsets of R
3 The extended real numbers
4 Sequences of real numbers
5 Open and closed sets of real numbers
6 Continuous functions
7 Borel sets
3 Lebesgue Measure
1 Introduction
2 Outer measure
3 Measurable sets and Lebesgue measure
4 A nonmeasurable set
5 Measurable functions
6 Littlewood's three principles
4 The Lebesgue Integral
1 The Riemann integral
2 The Legesgue integral of a bounded function over a set of
finite measure
3 The integral of a nonnegative function
4 The general Lebesgue integral
5 Convergence in measure
5 Differentiation and Integration
1 Differentiation of monotone functions
2 Functions of bounded variation
3 Differentiation of an integral
4 Absolute continuity
5 Convex functions
6 The Classical Banach Spaces
1 The L spaces
2 The Minkowski and Holder inequalities
3 Convergence and completeness
4 Approximation in L
5 Bounded linear functionals on the L spaces
Pate Two
ABSTRACT SPACES
7 Metric Spaces
1 introduction
2 Open and closed sets
3 Continuous functions and homeomorphisms
4 Convergence and completeness
5 Uniform continuity and uniformity
6 Subspaces
7 Compact metric spaces
8 Baire category
9 Absolute G's
10 The Ascoli-Arzela Theorem
8 Topological Spaces
1 Fundamental notions
2 Bases and countability
3 the separation axioms and continuous real-valued functions
4 Connectedness
5 Produces and direct unions of topolotical spaces
6 topological and uniform properties
7 Nets
9 Compact and Locally Compact Spaces
1 Compact spaces
2 Countable compactness and the Bolzano-Weierstrass property
3 Products of compact spaces
4 Locally compact spaces
5 compact spaces
6 Paracompact spaces
7 Manifolds
8 The Stone-Cech compactification
9 The Stone-Weierstrass Theorem
10 Banach Spaces
1 Introduction
2 Linear operators
3 Linear functionals and the Hahn-Banach Theorem
4 The Colsed Graph Theorem
5 Topological vector spaces
6 Weak topologies
7 Convexity
8 Hibert space
Part Three
GENERAL MEASURE AND INTEGRATION THEORY
11 Measure and Integration
1 Measure spaces
2 Measurable functions
3 Integration
4 General Convergence Theorems
5 Signed measures
6 The Radon-Nikodym Theorem
7 The L-spaces
12 Measure and Outer Measure
1 Outer measure and measurability
2 The Extension Theorem
3 The Lebesgue-Stigltjes integral
4 Product measures
5 Integral operators
6 Inner measure
7 Extension by sets of measure zero
8 Caratheodory outer measrue
9 Hausdorff measure
13 Measure and Topology
1 Baire sets and Borel sets
2 The regularity of Baire and Borel measures
3 The construction of Borel measures
4 Positive linear functionals and Borel measures
5 Bounded linear functionals on C(X)
14 Invariant Measures
1 Homogeneous spaces
2 Topological equicontinuity
3 The existence of invariant measure
4 Topological groups
5 Group actions and quotient spaces
6 Unicity of invariant measures
7 Groups of diffeomorphisms
15 Mappings of Measure Spaces
1 Point mappings and set mappings
2 Boolean algebras
3 Measure algebras
4 Borel equivalences
5 Borel measures on complete separable metric spaces
6 Set mappings and point mappings on complete separable
metric spaces
7 The isometries of L
16 The Daniell Integral
1 Intrlduction
2 The Extension Theorem
3 Uniqueness
4 Measurability and measure
Bibliography
Index of Symbols
Subject Index
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