Integral, Measure and Derivative: A Unified Approach (Dover Books on Mathematics) - Softcover

G. E. Shilov; B. L. Gurevich

Softcover

ISBN 10: 0486635198 ISBN 13: 9780486635194

Publisher: Dover Publications, 2012

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 this title

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.

Edition details

• Publisher: Dover Publications
• Publication date: 2012
• Language: English
• ISBN 10: 0486635198
• ISBN 13: 9780486635194
• Binding: Paperback
• Number of pages: 254