实分析
￥ 34.41 8.7折 ￥ 39.5 九五品
仅1件
作者(美)德贝内代托(DiBenedetto,E.) 著
出版社高等教育出版社
ISBN9787040226652
出版时间2007-10
版次1
装帧平装
开本16开
纸张胶版纸
页数485页
字数99999千字
定价39.5元
上书时间2024-12-26
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基本信息
书名:实分析
定价：39.50元
作者:(美)德贝内代托(DiBenedetto,E.) 著
出版社：高等教育出版社
出版日期：2007-10-01
ISBN：9787040226652
字数：560000
页码：485
版次：1
装帧：平装
开本：16开
商品重量：
编辑推荐
本书主要包含国外反映近代数学发展的纯数学与应用数学方面的书籍，天元基金邀请国内各个方向的知名数学家参与选题的工作，经专家遴选、推荐，由高等教育出版社影印出版。本书可作为高年级本科生教材或参考书。
内容提要
本书是一本内容十分翔实的实分析教材。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，Ascoli—Arzela定理， Calderon—Zygmund分解定理，Fefferman—Stein定理。Marcinkiewlcz插定理等实分析中有用的内容。 本书内容由浅入深。读者具有扎实的数学分析知识基础便可学习本书，学完本书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。
目录
PrefaceAcknowledgmentsPreliminaries 1 Countable sets 2 The Cantor set 3 Cardinality 3.1 Some examples 4 Cardinality of some infinite Cartesian products 5 Orderings, the mamal principle, and the aom of choice 6 Well-ordering 6.1 The first uncountable Problems and ComplementsⅠ Topologies and Metric Spaces 1 Topological spaces 1.1 Hausdorff and normal spaces 2 Urysohn's lemma 3 The Tietze extension theorem 4 Bases, aoms of countability, and product topologies 4.1 Product topologies 5 Compact topological spaces 5.1 Sequentially compact topological spaces 6 Compact subsets of RN 7 Continuous functions on countably compact spaces 8 Products of compact spaces 9 Vector spaces 9.1 Convex sets 9.2 Linear maps and isomorphisms 10 Topological vector spaces 10.1 Boundedness and continuity 11 Linear functionals 12 Finite-dimensional topological vector spaces 12.1 Locally compact spaces 13 Metric spaces 13.1 Separation and aoms of countability 13.2 Equivalent metrics 13.3 Pseudometrics 14 Metric vector spaces 14.1 Mapetween 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 ComplementsⅡ 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 IntegralⅣ Topics on Measurable Functions of Real VariablesⅤ The Lp(E)SpacesⅥ Banach SpacesⅦ Spaces of Continuous Functions,Distributions,and WeakⅧ Topics on Integrable Functions of Real VariablesⅨ Embeddings of W1,p(E)into Lq(E)ReferencesIndex
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