Measure and Integral

By

Rating

Product Description

Product Details

Preface to the Second Edition

Preface to the First Edition

Authors Preliminaries Points and Sets in R^{n}
^{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} ^{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} ^{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}
^{Lebesgue Measurable Functions}
^{Elementary Properties of Measurable
Functions} ^{Semicontinuous
Functions} ^{Properties of Measurable
Functions and Theorems of Egorov and Lusin}
^{Convergence in Measure}
^{Exercises} ^{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 Repeated
Integration Fubini's
Theorem Tonelli's
Theorem Applications of Fubini's
Theorem Exercises
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
Lp Classes
Definition of Lp
Hoelder'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
Approximations of the Identity
and Maximal Functions
Convolutions
Approximations of the
Identity
The Hardy-Littlewood Maximal
Function
The Marcinkiewicz
Integral
Exercises
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
Outer Measure and
Measure
Constructing Measures from
Outer Measures
Metric Outer
Measures
Lebesgue-Stieltjes
Measure
Hausdorff
Measure
Caratheodory-Hahn Extension
Theorem
Exercises
A Few Facts from Harmonic
Analysis
Trigonometric Fourier
Series
Theorems about Fourier
Coefficients
Convergence of
S[f] and
STH[f]
Divergence of Fourier
Series
Summability of Sequences and
Series
Summability of
S[f] and STH[f] by the Method of the
Arithmetic Mean
Summability of
S[f] by Abel
Means
Existence of f
TH
Properties of f TH for
f Lp, 1 < p
<
Application of Conjugate
Functions to Partial Sums of
S[f]
Exercises
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
Fractional
Integration
Subrepresentation
Formulas and Fractional
Integrals
L1,
L1 Poincare Estimates and the
Subrepresentation Formula; Hoelder
Classes
Norm
Estimates for I
Exponential
Integrability of I
f
Bounded
Mean
Oscillation
Exercises
Weak
Derivatives and Poincare-Sobolev
Estimates
Weak
Derivatives
Approximation
by Smooth Functions and Sobolev
Spaces
Poincare-Sobolev
Estimates
Exercises
Notations
Index}

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.

This item has low availability through normal channels. The supplier has a low reliability rating in Fishpond's system and may not arrive on time. Learn more.

Ask a Question About this Product More... |

Look for similar items by category

People also searched for

How Fishpond Works

Fishpond works with suppliers all over the world to bring you a huge selection of products, really great prices, and delivery included on over 25 million products that we sell.
We do our best every day to make Fishpond an awesome place for customers to shop and get what they want — all at the best prices online.

Webmasters, Bloggers & Website Owners

You can earn a 8%
commission by selling Measure and Integral: An Introduction to Real Analysis, Second Edition (Chapman & Hall/CRC Pure and Applied Mathematics)
on your website. It's easy to get started - we will give you example code.
After you're set-up, your website can earn you money while you work, play or even sleep!
You should start right now!

Authors / Publishers

Item ships from and is sold by Fishpond Retail Limited.

↑

Back to top