实分析（影印版）
2007-10
高等教育
德贝内代托
485
无
为了更好地借鉴国外数学教育与研究的成功经验，促进我国数学教育与研究事业的发展，提高高等学校数学教育教学质量，本着“为我国热爱数学的青年创造一个较好的学习数学的环境”这一宗旨，天元基金赞助出版“天元基金影印数学丛书”。 该丛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优秀书籍，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。为了提高我国数学研究生教学的水平，暂把选书的目标确定在研究生教材上。当然，有的书也可作为高年级本科生教材或参考书，有的书则介于研究生教材与专著之间。 欢迎各方专家、读者对本丛书的选题、印刷、销售等工作提出批评和建议。
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。
PrefaceAcknowledgmentsPreliminaries 1 Countable sets 2 The Cantor set 3 Cardinality 3.1 Some examples 4 Cardinality of some infinite Cartesian products 5 Orderings, the maximal principle, and the axiom 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, axioms 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 axioms of countability 13.2 Equivalent 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 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
《实分析（影印版）》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优秀书籍，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。《实分析（影印版）》可作为高年级本科生教材或参考书。
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数学专业很好的专业书。
内容很丰富, 但是在330~350之间有几页有黄色油迹, 似乎是印刷问题.