Integral Measure and Derivative: A Unified Approach

Integral Measure and Derivative: A Unified Approach

Paperback Dover Books on Mathematics Language: English / Russian

By (author) Georgi E. Shilov, By (author) Boris L. Gurevich, Volume editor Richard A. Silverman

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  • Publisher: Dover Publications Inc.
  • Format: Paperback | 256 pages
  • Language: English / Russian
  • Dimensions: 142mm x 208mm x 15mm | 272g
  • Publication date: 17 May 2012
  • Publication City/Country: New York
  • ISBN 10: 0486635198
  • ISBN 13: 9780486635194
  • Edition: New edition
  • Edition statement: New edition
  • Illustrations note: black & white illustrations
  • Sales rank: 440,309

Product description

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.

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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