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Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC P...
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A book that has been read but is in excellent condition. No obvious damage to the cover, with the dust jacket included for hard covers. No missing or damaged pages, no creases or tears, and no underlining/highlighting of text or writing in the margins. May be very minimal identifying marks on the inside cover. Very minimal wear and tear.
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eBay item number:286442006810
Item specifics
- Condition
- Release Year
- 1977
- Book Title
- Measure and Integral: An Introduction to Real Analysis (Chapma...
- ISBN
- 9780824764999
About this product
Product Identifiers
Publisher
CRC Press LLC
ISBN-10
0824764994
ISBN-13
9780824764999
eBay Product ID (ePID)
486484
Product Key Features
Number of Pages
288 Pages
Language
English
Publication Name
Measure and Integral : an Introduction to Real Analysis
Publication Year
1977
Subject
Functional Analysis, Calculus
Type
Textbook
Subject Area
Mathematics
Series
Chapman and Hall/Crc Pure and Applied Mathematics Ser.
Format
Hardcover
Dimensions
Item Height
0.8 in
Item Weight
19.2 Oz
Item Length
9.4 in
Item Width
6.2 in
Additional Product Features
Intended Audience
College Audience
LCCN
77-014167
Series Volume Number
308
Illustrated
Yes
Dewey Decimal
515/.42
Table Of Content
Preliminaries Points and Sets in Rn Rn as a Metric Space Open and Closed Sets in Rn: Special Sets Compact Sets; The Heine-Borel Theorem Functions Continuous Functions and Transformations The Riemann Integral Exercises Function of Bounded Variation; The Riemann-Stieltjes Integral Functions of Bounded Variation Rectifiable Curves The Reiman-Stieltjes Integral Further Results About the Reimann-Stieltjes Integrals Exercises Lebesgue Measure and Outer Measure Lebesgue Outer Measures; 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; Egorov's Theorem and Lusin's Theorem 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 A Relation Between Riemann-Stieltjes and Lebesgue Integrals; the LP Spaces, 0
Synopsis
This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given. Closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, L(p)) classes, and various results about differentiation are examined in detail. Several applications of the theory to a specific branch of analysis--harmonic analysis--are also provided. Among these applications are basic facts about convolution operators and Fourier series, including results for the conjugate function and the Hardy-Littlewood maximal function. Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis for student interested in mathematics, statistics, or probability. Requiring only a basic familiarity with advanced calculus, this volume is an excellent textbook for advanced undergraduate or first-year graduate student in these areas., This volume develops the classical theory of the Lebesgue integral and some of its applications. Following a thorough study of the concepts of outer measure and measure, the author initially presents the integral in the context of n-dimensional Euclidean space. A more general treatment of the integral, based on an axiomatic approach, is given later. The book examines closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, L(p) classes, and various results about differentiation. Several applications of the theory to a specific branch of analysis-harmonic analysis-are also provided.
LC Classification Number
QA312 .W43
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