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Measure and Integral: An Introduction to Real Analysis, 2nd  무료배송

 
지은이 : Richard L. Wheeden & Antoni Zygmund
출판사 : CRC Press
판수 : 2nd(2015)
페이지수 : 532
ISBN : 9781498702898
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 49,000원 ( 무료배송 )
적립금 : 1,470 Point
     

 

Richard L. Wheeden is Distinguished Professor of Mathematics at Rutgers University, New Brunswick, New Jersey, USA. His primary research interests lie in the fields of classical harmonic analysis and partial differential equations, and he is the author or coauthor of more than 100 research articles. After earning his Ph.D. from the University of Chicago, Illinois, USA (1965), he held an instructorship there (1965–1966) and a National Science Foundation (NSF) Postdoctoral Fellowship at the Institute for Advanced Study, Princeton, New Jersey, USA (1966–1967).


Antoni Zygmund was Professor of Mathematics at the University of Chicago, Illinois, USA. He was earlier a professor at Mount Holyoke College, South Hadley, Massachusetts, USA, and the University of Pennsylvania, Philadelphia, USA. His years at the University of Chicago began in 1947, and in 1964, he was appointed Gustavus F. and Ann M. Swift Distinguished Service Professor there. He published extensively in many branches of analysis, including Fourier series, singular integrals, and differential equations. He is the author of the classical treatise Trigonometric Series and a coauthor (with S. Saks) of Analytic Functions. He was elected to the National Academy of Sciences in Washington, District of Columbia, USA (1961), as well as to a number of foreign academies.

Preface to the Second Edition
Preface to the First Edition
Authors

1.Preliminaries
Points and Sets in Rn
Rn as a Metric Space
Open and Closed Sets in Rn, and Special Sets
Compact Sets and the Heine–Borel Theorem
Functions
Continuous Functions and Transformations
The Riemann Integral
Exercises


2.Functions of Bounded Variation and the Riemann–Stieltjes Integral
Functions of Bounded Variation
Rectifiable Curves
The Riemann–Stieltjes Integral
Further Results about Riemann–Stieltjes Integrals
Exercises


3.Lebesgue Measure and Outer Measure
Lebesgue Outer Measure and the Cantor Set
Lebesgue Measurable Sets
Two Properties of Lebesgue Measure
Characterizations of Measurability
Lipschitz Transformations of Rn
A Nonmeasurable Set
Exercises


4.Lebesgue Measurable Functions
Elementary Properties of Measurable Functions
Semicontinuous Functions
Properties of Measurable Functions and Theorems of Egorov and Lusin
Convergence in Measure
Exercises


5.The Lebesgue Integral
Definition of the Integral of a Nonnegative Function
Properties of the Integral
The Integral of an Arbitrary Measurable f
Relation between Riemann–Stieltjes and Lebesgue Integrals, and the Lp Spaces, 0 < p < ∞
Riemann and Lebesgue Integrals
Exercises


6.Repeated Integration
Fubini’s Theorem
Tonelli’s Theorem
Applications of Fubini’s Theorem
Exercises


7.Differentiation
The Indefinite Integral
Lebesgue’s Differentiation Theorem
Vitali Covering Lemma
Differentiation of Monotone Functions
Absolutely Continuous and Singular Functions
Convex Functions
The Differential in Rn
Exercises


8.Lp Classes
Definition of Lp
Hölder’s Inequality and Minkowski’s Inequality
Classes l p
Banach and Metric Space Properties
The Space L2 and Orthogonality
Fourier Series and Parseval’s Formula
Hilbert Spaces
Exercises


9.Approximations of the Identity and Maximal Functions
Convolutions
Approximations of the Identity
The Hardy–Littlewood Maximal Function
The Marcinkiewicz Integral
Exercises


10.Abstract Integration
Additive Set Functions and Measures
Measurable Functions and Integration
Absolutely Continuous and Singular Set Functions and Measures
The Dual Space of Lp
Relative Differentiation of Measures
Exercises


11.Outer Measure and Measure
Constructing Measures from Outer Measures
Metric Outer Measure
Lebesgue–Stieltjes Measure
Hausdorff Measure
Carathéodory–Hahn Extension Theorem
Exercises


12.A Few Facts from Harmonic Analysis
Trigonometric Fourier Series
Theorems about Fourier Coefficients
Convergence of S[f] and [f]
Divergence of Fourier Series
Summability of Sequences and Series
Summability of S[f] and [f] by the Method of the Arithmetic Mean
Summability of S[f] by Abel Means
Existence of f Þ
Properties of f Þ for fLp, 1 < p < ∞
Application of Conjugate Functions to Partial Sums of S[f]
Exercises


13.The Fourier Transform
The Fourier Transform on L1
The Fourier Transform on L2
The Hilbert Transform on L2
The Fourier Transform on Lp, 1 < p < 2
Exercises


14.Fractional Integration
Subrepresentation Formulas and Fractional Integrals
L1, L1 Poincaré Estimates and the Subrepresentation Formula; Hölder Classes
Norm Estimates for Iα
Exponential Integrability of Iαf
Bounded Mean Oscillation
Exercises


15.Weak Derivatives and Poincaré–Sobolev Estimates
Weak Derivatives
Approximation by Smooth Functions and Sobolev Spaces
Poincaré–Sobolev Estimates
Exercises

Notations


Index

Introduction to Partial Di...
-Zachmanoglou-
 
 
Real Analysis Modern Techn...
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A First Course in Abstract...
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