Integral, Measure and Derivative: A Unified Approach

Integral, Measure and Derivative: A Unified Approach

by Georgii Evgenevich Shilov

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Overview

Integral, Measure and Derivative: A Unified Approach by Georgii Evgenevich Shilov


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.

Product Details

ISBN-13: 9780486635194
Publisher: Dover Publications
Publication date: 05/17/2012
Series: Dover Books on Mathematics Series
Edition description: Rev. English ed
Pages: 256
Sales rank: 1,227,826
Product dimensions: 5.62(w) x 8.22(h) x 0.50(d)

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