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25 Remote Warehouse Mathematics- Calculus

Integral, Measure and Derivative: A Unified Approach (Dover Books on Mathematics)

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Integral, Measure and Derivative: A Unified Approach (Dover Books on Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

This graduate-level textbook and monograph defines the functions of a real variable through consistent use of the Daniell scheme, offering a rare and useful alternative to customary approaches. The treatment can be understood by any reader with a solid background in advanced calculus, and it features many problems with hints and answers. "The exposition is fresh and sophisticated," declared Sci-Tech Book News, "and will engage the interest of accomplished mathematicians."

Part one is devoted to the integral, moving from the Reimann integral and step functions to a general theory, and obtaining the "classical" Lebesgue integral in n space. Part two constructs the Lebesgue-Stieltjes integral through the Daniell scheme using the Reimann-Stieltjes integral as the elementary integral. Part three develops theory of measure with the general Daniell scheme, and the final part is devoted to the theory of the derivative.

Synopsis:

This treatment examines the general theory of the integral, Lebesque integral in n space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.

Table of Contents

Introduction
Part 1 The Integral
1. The Riemann Integral and Step Functions
2. General Theory of the Integral
3. The Lebesgue Integral in n-Space
Part 2 The Stieltjes Integral
4. The Riemann-Stieltjes Integral
5. The Lebesgue-Stieltjes Integral
6. Measurable Sets and General Measure Theory
7. Construtive Measure Theory
8. Axiomatic Measure Theory
9. Measure and Set Functions
10. The Derivative of a Set Function
Bibliography
Index
 

Product Details

ISBN:
9780486635194
Translator:
Silverman, Richard A.
Publisher:
Dover Publications
Author:
Mathematics
Author:
Gurevich, B. L.
Author:
Shilov, G. E.
Location:
New York :
Subject:
Mathematics
Subject:
Measure theory
Subject:
Advanced
Subject:
Mathematics-Calculus
Edition Number:
Rev. English ed.
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20120531
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
254
Dimensions:
8.25 x 5.63 in

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Related Subjects

Engineering » Engineering » General Engineering
Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General

Integral, Measure and Derivative: A Unified Approach (Dover Books on Mathematics) New Trade Paper
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Product details 254 pages Dover Publications - English 9780486635194 Reviews:
"Synopsis" by ,
This treatment examines the general theory of the integral, Lebesque integral in n space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.
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