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內容簡介

　　《實分析教程（第2版）》是一部備受專傢好評的教科書，書中用現代的方式清晰論述瞭實分析的概念與理論，定理證明簡明易懂，可讀性強，全書共有200道例題和1200例習題。《實分析教程（第2版）》的寫法像一部文學讀物，這在數學教科書很少見，因此閱讀《實分析教程（第2版）》會是一種享受。

作者簡介

　　麥剋唐納（John N.McDonald），McDonald After receiving his Ph.D.in mathematics from Rut gers University, John N.McDonald joined the faculty in the Department of Mathematics （now the School of Mathematical and Statistical Scrences） at Arizona State University, where he attained the rank of full professor.McDonald has taught a wide range of mathematics courses, including calculus, linear algebra, difFerential equations, real analysis, complexanalysis, and functional analysis.Known by colleagues and students alike as an excelient instructor, McDonald was honored by his department with the Charles Wexler Teaching Award.He also serves as a mentor in the prestigious Joaquin Bustoz Math-Saence Honors Program, an intense academic program that pfovides motivated students an opportunity to commence university mathematics and science studies prior to graduating high school. McDonald has numerous research pubHcations, which span the areas of complex analysist functional analysis, harmonic analysis, and probability theory.He is also a former Managing Fditor of the Rocky Mountain Journal of Mathematics.McDonald and his wife, Pat, have four children and six grandchildren.In addition to spending time with his family, he enjoys music, film, and staying physically fit through jogging and other exercising.

內頁插圖

目錄

About the Authors Preface
PART ONE. Set Theory， Real Numbers， and Calculus
1. SET THEORY Biography： Georg Cantor
1.1 Basic Definitions and Properties
1.2 Functions and Sets
1.3 Equivalence of Sets； Countability
1.4 Algebras， a-Algebras， and Monotone Classes
2. THE REAL NUMBER SYSTEM AND CALCULUS
Biography： Georg Friedrich Bernhard Riemann
2.1 The ReaINumber System
2.2 Sequences of Real Numbers
2.3 Open and Closed Sets
2.4 Real-Valued Functions
2.5 The Cantor Set and Cantor Function
2.6 The Riemann Integral

PART TWO. Measure， Integration， and DifFerentiation
3. LEBESGUE MEASURE ON THE REAL LINE
Biography： Emile Felix-Edouard-Justrn Borel
3.1 Borel Measurable Functions and Borel Sets
3.2 Lebesgue Outer Measure
3.3 Further Properties of Lebesgue Outer Measure
3.4 Lebesgue Measure
4. THE LEBESGUE INTEGRAL ON THE REAL LINE
Biography： Henri Leon Lebesgue
4.1 The Lebesgue Integral for Nonnegative Functions
4.2 Convergence Properties of the Lebesgue Integral for Nonnegative Functions
4.3 The General Lebesgue Integral
4.4 Lebesgue Almost Everywhere
5. ELEMENTS OF MEASURE THEORY
Biography： Constantin Caratheodory
5.1 MeasureSpaces
5.2 Measurable Functions
5.3 The Abstract Lebesgue Integral for Nonnegative Functions
5.4 The General Abstract Lebesgue Integral
5.5 Convergence in Measure
6 .EXTENSIONS TO MEASURES AND PRODUCT MEASURE
Biography： Guido Fubini
6.1 Extensions to Measures
6.2 The Lebesgue-Stieltjes Integral
6.3 Product Measure Spaces
6.4 Iteration oflntegrals in Product Measure Spaces
7. ELEMENTS OF PROBABILITY
Biography： Andrei Niko/aewch Kolmogorov
7.1 The Mathematical Model for Probability
7.2 Random Variables
7.3 Expectation of Random Variables
7.4 The Law of Large Numbers
……

PART THREE. Topological， Metric， and Normed Spaces
PART FOUR. Harmonic Analysis， DynamicaISystems， and Hausdorff Measure

前言/序言

　　This book is about real analysis， but it is not an ordinary real analysis book. Written with the student in mind， it incorporates pedagogical techniques not often found in books at this level.
　　In brief， A Corse in Real Analysis is a modern graduate-level or advanced- undergraduate-level textbook about real analysis that engages its readers with motivation of key concepts， hundreds of examples， over 1300 exercises， and ap- plica.tions to probability and statistics， Fourier analysis， wavelets， measurable dynanucal 8ystems， Hausdorff measure， and fractals.
　　What Makes This Book Unique　
　　A Course in， Real Analysis contains many features that are unique for a real analysis text. Here are some of those features.
　　Motivation of key concepts. All key concepts are motivated.　The importance of and rationale behind ideas such as measurable functions， measurable sets， and Lebesgue integration are made transparent.
　　Detailed theoretical discuspion. Detailed proo's of most results （i.e.， lem- mas， theorems， corollaries， and propositions） are provided. To fully engage the reader， proofs or parts of proofs are sometimes assigned as exercises.
　　Illustrative examples. Following most definitions and results， one or more examples， most of which consist of several parts， are presented that illustrate the concept or result in order to solidify it in the reader's mind and provide a concrete frame of reference.

實分析教程（第2版） [A Course in Real Analysis] 下載 mobi epub pdf txt 電子書

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