Integral, Measure and Derivative

A Unified Approach

Nonfiction, Science & Nature, Mathematics
Cover of the book Integral, Measure and Derivative by G. E. Shilov, B. L. Gurevich, Dover Publications
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Author: G. E. Shilov, B. L. Gurevich ISBN: 9780486165615
Publisher: Dover Publications Publication: May 13, 2013
Imprint: Dover Publications Language: English
Author: G. E. Shilov, B. L. Gurevich
ISBN: 9780486165615
Publisher: Dover Publications
Publication: May 13, 2013
Imprint: Dover Publications
Language: English
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.
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
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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