ENGLISH

Integral, Measure and Derivative: A Unified Approach

By G. E. Shilov , B. L. Gurevich

Book information

Publisher
Dover Publications
ISBN
0486635198, 9780486635194
Language
english
Format
PDF
Filesize
11 MB (11930936 bytes)
Series
Dover Books on Mathematics
Pages
C, xiv, 233, B\250
Orientation
portrait
Paginated
yes
Scanned
yes
Time added
2014-11-19 09:51:40

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.Reprint of the English translation, Prentice-Hall, Inc., Upper Saddle River, New Jersey, 1966.

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