Selected Problems in Real Analysis (Translations of Mathematical Monographs, 107)

This book is intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area. It differs from other problem books in the greater difficulty of the problems, some of which are well-known theorems in analysis. Nonetheless, no special preparation is required to solve the majority of the problems. Brief but detailed solutions to most of the problems are given in the second part of the book. This book is unique in that the authors have aimed to systematize a range of problems that are found in sources that are almost inaccessible (especially to students) and in mathematical folklore. Readership: Graduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis. Table of Contents Introduction Sequences Functions Series Integrals Asymptotics Functions (continuation) Lebesgue measure and the Lebesgue integral Sequences of measurable functions Iterates of transformations of an interval Answers Intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area, this title contains problems, some of which are well-known theorems in analysis. It also includes brief but detailed solutions to most of the problems.