Integral, Measure and Derivative: A Unified Approach

ISBN-13: 9780486635194 / Angielski / Miękka / 2012 / 254 str.

G. E. Shilov; B. L. Gurevich;Mathematics

Opis

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.