實(shí)分析（影印版）

前言

　　為了更好地借鑒國(guó)外數(shù)學(xué)教育與研究的成功經(jīng)驗(yàn)，促進(jìn)我國(guó)數(shù)學(xué)教育與研究事業(yè)的發(fā)展，提高高等學(xué)校數(shù)學(xué)教育教學(xué)質(zhì)量，本著“為我國(guó)熱愛數(shù)學(xué)的青年創(chuàng)造一個(gè)較好的學(xué)習(xí)數(shù)學(xué)的環(huán)境”這一宗旨，天元基金贊助出版“天元基金影印數(shù)學(xué)叢書”。　　該叢書主要包含國(guó)外反映近代數(shù)學(xué)發(fā)展的純數(shù)學(xué)與應(yīng)用數(shù)學(xué)方面的優(yōu)秀書籍，天元基金邀請(qǐng)國(guó)內(nèi)各個(gè)方向的知名數(shù)學(xué)家參與選題的工作，經(jīng)專家遴選、推薦，由高等教育出版社影印出版。為了提高我國(guó)數(shù)學(xué)研究生教學(xué)的水平，暫把選書的目標(biāo)確定在研究生教材上。當(dāng)然，有的書也可作為高年級(jí)本科生教材或參考書，有的書則介于研究生教材與專著之間。　　歡迎各方專家、讀者對(duì)本叢書的選題、印刷、銷售等工作提出批評(píng)和建議。

內(nèi)容概要

本書是一本內(nèi)容十分翔實(shí)的實(shí)分析教材。它包含集論，點(diǎn)集拓?fù)?。測(cè)度與積分，Lebesgue函數(shù)空間，Banach空間與Hilbert空間，連續(xù)函數(shù)空間，廣義函數(shù)與弱導(dǎo)數(shù)，Sobolev空間與Sobolev嵌入定理等；同時(shí)還包含 Lebesgue微分定理，Stone-Weierstrass逼近定理，Ascoli—Arzela定理， Calderon—Zygmund分解定理，F(xiàn)efferman—Stein定理。Marcinkiewlcz插定理等實(shí)分析中有用的內(nèi)容?！　”緯鴥?nèi)容由淺入深。讀者具有扎實(shí)的數(shù)學(xué)分析知識(shí)基礎(chǔ)便可學(xué)習(xí)本書，學(xué)完本書的讀者將具備學(xué)習(xí)分析所需要的實(shí)變與泛函(不包括算子理論)的準(zhǔn)備知識(shí)和訓(xùn)練。

書籍目錄

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

編輯推薦

　　《實(shí)分析（影印版）》主要包含國(guó)外反映近代數(shù)學(xué)發(fā)展的純數(shù)學(xué)與應(yīng)用數(shù)學(xué)方面的優(yōu)秀書籍，天元基金邀請(qǐng)國(guó)內(nèi)各個(gè)方向的知名數(shù)學(xué)家參與選題的工作，經(jīng)專家遴選、推薦，由高等教育出版社影印出版?！秾?shí)分析（影印版）》可作為高年級(jí)本科生教材或參考書。

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