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　　《實分析（影印版）》主要包含國外反映近代數學發展的純數學與應用數學方麵的優秀書籍，天元基金邀請國內各個方嚮的知名數學傢參與選題的工作，經專傢遴選、推薦，由高等教育齣版社影印齣版。《實分析（影印版）》可作為高年級本科生教材或參考書。

內容簡介

　　《實分析（影印版）》是一本內容十分翔實的實分析教材。它包含集論，點集拓撲。測度與積分，Lebesgue函數空間，Banach空間與Hilbert空間，連續函數空間，廣義函數與弱導數，Sobolev空間與Sobolev嵌入定理等；同時還包含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插定理等實分析中有用的內容。
　　《實分析（影印版）》內容由淺入深。讀者具有紮實的數學分析知識基礎便可學習《實分析（影印版）》，學完《實分析（影印版）》的讀者將具備學習分析所需要的實變與泛函（不包括算子理論）的準備知識和訓練。

內頁插圖

目錄

Preface
Acknowledgments
Preliminaries
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 Complements

Ⅰ Topologies and Metric Spaces
1 Topological spaces
1.1 Hausdorff and normal spaces
2 Urysohns 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 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

14 Borel sets, measurable sets, and incomplete measures
14.1 A continuous increasing function f : [0, 1] → [0, 1]
14.2 On the preimage of a measurable set
14.3 Proof of Propositions 14.1 and 14.2

15 More on Borel measures
15.1 Some extensions to general Borel measures
15.2 Regular Borel measures and Radon measures

16 Regular outer measures and Radon measures
16.1 More on Radon measures
17 Vitali coverings
18 The Besicovitch covering theorem
19 Proof of Proposition 18.2
20 The Besicovitch measure-theoretical covering theorem
Problems and Complements

Ⅲ The Lebesgue Integral
1 Measurable functions
2 The Egorov theorem
2.1 The Egorov theorem in RN
2.2 More on Egorovs theorem
3 Approximating measurable functions by simple functions
4 Convergence in measure
5 Quasi-continuous functions and Lusins theorem
6 Integral of simple functions
7 The Lebesgue integral of nonnegative functions
8 Fatous lemma and the monotone convergence theorem
9 Basic properties of the Lebesgue integral
10 Convergence theorems
11 Absolute continuity of the integral
12 Product of measures
13 On the structure of （A*p ）
14 The Fubini-Tonelli theorem
14.1 The Tonelli version of the Fubini theorem

15 Some applications of the Fubini-Tonelli theorem
15.1 Integrals in terms of distribution functions
15.2 Convolution integrals
15.3 The Marcinkiewicz integral
16 Signed measures and the Hahn decomposition
17 The Radon-Nikodym theorem

18 Decomposing measures
18.1 The Jordan decomposition
18.2 The Lebesgue decomposition
18.3 A general version of the Radon-Nikodym theorem
Problems and Complements

IV Topics on Measurable Functions of Real Variables
1 Functions of bounded variations
2 Dini derivatives
3 Differentiating functions of bounded variation
4 Differentiating series of monotone functions
5 Absolutely continuous functions
6 Density of a measurable set
7 Derivatives of integrals
8 Differentiating Radon measures
9 Existence and measurability of Dvv
9.1 Proof of Proposition 9.2
10 Representing Dvv
10.1 Representing Duv for v << #
10.2 Representing Duv for v u

11 The Lebesgue differentiation theorem
11.1 Points of density
11.2 Lebesgue points of an integrable function
12 Regular families
13 Convex functions
14 Jensens inequality
15 Extending continuous functions
16 The Weierstrass approximation theorem
17 The Stone-Weierstrass theorem

18 Proof of the Stone-Weierstrass theorem
18.1 Proof of Stones theorem
19 The Ascoli-Arzela theorem
19.1 Precompact subsets of C（E）
Problems and Complements

V The LP（E） Spaces
1 Functions in Lp（E） and their norms
1.1 The spaces LP for 0 < p < 1
1.2 The spaces Lq for q < 0
2 The HOlder and Minkowski inequalities
3 The reverse Holder and Minkowski inequalities
4 More on the spaces Lp and their norms
4.1 Characterizing the norm fp for 1 < p < oo
4.2 The norm II I1 for E of finite measure
4.3 The continuous version Of the Minkowski inequality

5 LP（E） for 1 < p < oo as normed spaces of equivalence classes
5.1 Lp（E） for 1 < p < as ametric topological vector space

6 A metric topology for LP（E） when 0 < p < 1
6.1 Open convex subsets of LP （E） when0 < p < 1
7 Convergence in LP（E） and completeness
8 Separating LP（E） by simple functions

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

前言/序言

　　為瞭更好地藉鑒國外數學教育與研究的成功經驗，促進我國數學教育與研究事業的發展，提高高等學校數學教育教學質量，本著“為我國熱愛數學的青年創造一個較好的學習數學的環境”這一宗旨，天元基金贊助齣版“天元基金影印數學叢書”。
　　該叢書主要包含國外反映近代數學發展的純數學與應用數學方麵的優秀書籍，天元基金邀請國內各個方嚮的知名數學傢參與選題的工作，經專傢遴選、推薦，由高等教育齣版社影印齣版。為瞭提高我國數學研究生教學的水平，暫把選書的目標確定在研究生教材上。當然，有的書也可作為高年級本科生教材或參考書，有的書則介於研究生教材與專著之間。
　　歡迎各方專傢、讀者對本叢書的選題、印刷、銷售等工作提齣批評和建議。
實分析（影印版） [Real Analysis] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

不錯，價格便宜，內容不錯

評分☆☆☆☆☆

很好的實變函數的入門書。講解很清晰！

評分☆☆☆☆☆

很不錯的研究生分析教材

評分☆☆☆☆☆

《實分析（影印版）》是一本內容十分翔實的實分析教材。它包含集論，點集拓撲。測度與積分，Lebesgue函數空間，Banach空間與Hilbert空間，連續函數空間，廣義函數與弱導數，Sobolev空間與Sobolev嵌入定理等；同時還包含Lebesgue微分定理，Stone-Weierstrass逼近定理，Ascoli&mdash;Arzela定理，Calderon&mdash;Zygmund分解定理，Fefferman&mdash;Stein定理。Marcinkiewlcz插定理等實分析中有用的內容。

評分☆☆☆☆☆

《實分析（影印版）》主要包含國外反映近代數學發展的純數學與應用數學方麵的優秀書籍，天元基金邀請國內各個方嚮的知名數學傢參與選題的工作，經專傢遴選、推薦，由高等教育齣版社影印齣版。《實分析（影印版）》可作為高年級本科生教材或參考書。

評分☆☆☆☆☆

買來學習數學的，價格還算實惠，在這裏買書越來越貴瞭啊，不像以前那樣瘋狂瞭啊，這個書送來時封皮是有磨損的，希望以後不要這樣啊。

評分☆☆☆☆☆

《實分析（影印版）》主要包含國外反映近代數學發展的純數學與應用數學方麵的優秀書籍，天元基金邀請國內各個方嚮的知名數學傢參與選題的工作，經專傢遴選、推薦，由高等教育齣版社影印齣版。《實分析（影印版）》可作為高年級本科生教材或參考書。

評分☆☆☆☆☆

材逐步代替瞭原先采用的蘇聯教材，但還在很大程度上保留著蘇聯教材的影響，同時，一些蘇聯教材仍被廣大教師和學生作為主要參考書或課外讀物繼續發揮著作用。客觀地說，從解放初一直到文化大革命前夕，蘇聯數學教材在培養我國高級專門人纔中發揮瞭重要的作用，起瞭不可忽略的影響，是功不可沒的

評分☆☆☆☆☆

材逐步代替瞭原先采用的蘇聯教材，但還在很大程度上保留著蘇聯教材的影響，同時，一些蘇聯教材仍被廣大教師和學生作為主要參考書或課外讀物繼續發揮著作用。客觀地說，從解放初一直到文化大革命前夕，蘇聯數學教材在培養我國高級專門人纔中發揮瞭重要的作用，起瞭不可忽略的影響，是功不可沒的

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