(Download) "Integral, Measure and Derivative" by G. E. Shilov & B. L. Gurevich # eBook PDF Kindle ePub Free

eBook details

Title: Integral, Measure and Derivative
Author : G. E. Shilov & B. L. Gurevich
Release Date : January 13, 2013
Genre: Mathematics,Books,Science & Nature,
Pages : * pages
Size : 24437 KB

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.