Title: Integral, Measure and Derivative: A Unified Approach (Paperback or Softback)
Publisher: Dover Publications 5/17/2012
Publication Date: 2012
Language: English
ISBN 10: 0486635198
ISBN 13: 9780486635194
Binding: Paperback or Softback
Condition: New
Weight: 0.5 pounds
Book Type: Book

About this title

Synopsis

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.

About the Author

Georgi Evgen'evich Shilov (1917–75) was a Soviet mathematician and an expert in the field of functional analysis who contributed to the theory of normed rings and generalized functions. He is the author of five Dover books.
B. L. Gurevich was a Soviet mathematician.

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Integral, Measure and Derivative: A Unified Approach (Paperback or Softback)

Shilov, G. E.

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