Measure, Integral, Derivative [electronic resource] : A Course on Lebesgue's Theory / by Sergei Ovchinnikov.

1 Preliminaries -- 2 Lebesgue Measure -- 3 Lebesgue Integration -- 4 Differentiation and Integration -- A Measure and Integral over Unbounded Sets -- Index.

This classroom-tested text is intended for a one-semester course in Lebesgues theory. With over 180 exercises, the texttakes an elementary approach, making iteasily accessible toboth upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where -algebras are not used in the text on measure theory and Dinis derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgues theory are found in the book.

ZDB-2-SMA