Integral, Measure, and Derivative: A Unified Approach

Book Details:

• Publisher: Dover

• Author: Georgii Evgenevich Shilov

• Language: English

• Edition: Revised Edition

• ISBN: 9780486635194

• Pages: 256

• Cover: Paperback

• Dimensions: 8.5 x 5.4 x 0.7 inches

About the Book:

Functions of a Real Variable by Georgii Evgenevich Shilov is a graduate-level textbook that offers a unique approach to the theory of real-valued functions. Through the consistent application of the Daniell scheme, this book provides an alternative perspective to the traditional methods of defining functions, making it a valuable resource for advanced students and mathematicians alike.

The book is divided into four parts, each covering a different aspect of real analysis. Part one focuses on the integral, beginning with the Riemann integral and step functions, progressing to the general theory, and concluding with the "classical" Lebesgue integral in n-space. In part two, Shilov constructs the Lebesgue-Stieltjes integral using the Daniell scheme, starting with the elementary Riemann-Stieltjes integral. Part three introduces the theory of measure, also within the framework of the Daniell scheme, and part four delves into the theory of the derivative.

Designed for readers with a solid foundation in advanced calculus, this book features numerous problems with hints and answers to help deepen understanding. Praised for its fresh and sophisticated exposition by Sci-Tech Book News, Shilov’s work engages readers with its thought-provoking approach to real analysis, providing both theoretical depth and practical insights. This book is ideal for graduate students and professionals looking to explore real analysis from a novel and advanced perspective.