实分析

《实分析(影印版)》是2007年高等教育出版社出版的图书吧陆请察，作者是德贝内代托。

• 书名 实分析(影印版)
• 作者 德贝内代托
• 出版社 高等教育出版社
• 出版时间 2007年10月
• 页数 485 页

内容简介

　　《实分析(影印版)》是一本内容十分翔实的实分析来自教材。它包含集论，点集拓扑。测度与积分，Lebesgue函数空间，Banach空间与Hilbert空间，连续函数空间，广义函数与弱导数，Sobolev空间与Sobolev嵌入定理等;同时还包含Lebesgue微分定理，Stone-Weierstrass逼近定理，Ascol360百科i-Arzela定理，Calderon-Zygmu令妈植战没切侵精进nd分解定理，Fefferman-Stein定理。Marcinkiewlcz插定理等实分析中有用的内容。

　　《实分析(影印版)》内容由浅入深。读者具有扎实的数学分企从消析知识基础便可学习《实分析(影印版)》，学完《实分析(影印版)》的读者将具备学习分析所需要的实变与泛函(不包括算子理论)的准备知识和训练。

图书目录

　　Preface

　板士止批应啊始素　Acknowledgments

　　Preliminaries

耐燃全电令罪场宣弦　　1 Countable sets

　　2 The Cantor set

　　3 Ca即伤站州味刘非rdinality

　　3.1 Some examples

　　4 Cardinality of some infinite Cartesian products

　　5 Orderings, the maximal principle, and the axiom of 千害注斗孔个培静特choice

　　6 Well-ordering

　　6.1 The first uncountable

　　Problems and Complements

　　Ⅰ Topologies and Metric Spaces

　　1 Topological spaces

　　1.1 Hausdorff and normal spaces

　　2 Urysohn's lemma

　　3 The Tietze extension theorem

　　4 Bases, axioms o世f countability, a转同知缩弱激nd product to几目式百pologies

　　4.1 Product topologies

　　5 Compact topological space职s

　　5.1 Sequentially compact topological spaces

　　6 Compact subsets of RN

右赶设雷往　　7 Continuous functions on countably compact spaces

　　8 Products of compact spaces

　　9 Vector spaces

　　9.1 Con环序方随北封vex sets

　　9.2 Linear maps and isomorphisms

　　10 Topological vector spaces

　　10.1 Bo处阶脚undedness 台误虽没看and continuity

　　11 Linear functiona号讲ls

　　12 Finite-dimensional t组六火果沙扩opological vector spaces

　　12.1 Lo卷制绝cally compact spaces

　　13 Metric spaces

　　13.1 Separation and axioms of countability

　　13.2 Equ推压于统ivalent metrics

　　13.3 Pseudometrics

　　14 Metric vector spaces

　　14.1 Maps between metric spaces

　　15 Spaces of continuous functions

　　15.1 Spaces of continuously differentiable functions

　　16 On the structure of a complete metric space

　　17 Compact and totally bounded metric spaces

　　17.1 Precompact subsets of X

　　Problems and Complements

　　Ⅱ Measuring Sets

　　1 Partitioning open subsets of RN

　　2 Limits of sets, characteristic functions, and or-algebras

　　3 Measures

　　3.1 Finite,a-finite, and complete measures

　　3.2 Some examples

　　4 Outer measures and sequential coverings

　　4.1 The Lebesgue outer measure in RN

　　4.2 The Lebesgue-Stieltjes outer measure

　　5 The Hausdorff outer measure in RN

　　6 Constructing measures from outer measures

　　7 The Lebesgue--Stieltjes measure on R

　　7.1 Borel measures

　　8 The Hausdorff measure on RN

　　9 Extending measures from semialgebras to a-algebras

　　9.1 On the Lebesgue-Stieltjes and Hausdorff measures

　　10 Necessary and sufficient conditions for measurability

　　11 More on extensions from semialgebras to a-algebras

　　12 The Lebesgue measure of sets in RN

　　12.1 A necessary and sufficient condition of naeasurability

　　13 A nonmeasurable set

　　……

　　Ⅲ The Lebesgue Integral

　　Ⅳ Topics on Measurable Functions of Real Variables

　　Ⅴ The Lp(E)Spaces

　　Ⅵ Banach Spaces

　　Ⅶ Spaces of Continuous Functions,Distributions,and Weak

　　Ⅷ Topics on Integrable Functions of Real Variables

　　Ⅸ Embeddings of W1,p(E)into Lq(E)

　　References

　　Index