โ Scribed by Ovchinnikov, Sergei
No coin nor oath required. For personal study only.
This classroom-tested text is intended for a one-semester course in Lebesgueโs theory. ย With over 180 exercises, the textย takes an elementary approach, making itย easily accessible toย both upper-undergraduate- and lower-graduate-level students. ย 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. ย The presentation is elementary, where ฯ-algebras are not used in the text on measure theory and Diniโs derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgueโs theory are found in the book. http://online.sfsu.edu/sergei/MID.htm
๐ SIMILAR VOLUMES
Real Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications both classical and those rarely covered in literature. ย This book provides a detai