Problems in Mathematical Analysis III: Integration
About this Title
W. J. Kaczor, Marie Curie-Sklodowska University, Lublin, Poland and M. T. Nowak, Marie Curie-Sklodowska University, Lublin, Poland
Publication: The Student Mathematical Library
Publication Year 2003: Volume 21
ISBNs: 978-0-8218-3298-1 (print); 978-1-4704-2135-9 (online)
MathSciNet review: MR1998016
MSC: Primary 28-01; Secondary 00A07, 26-01
We learn by doing. We learn mathematics by doing problems. This is the third volume of Problems in Mathematical Analysis. The topic here is integration for real functions of one real variable. The first chapter is devoted to the Riemann and the Riemann-Stieltjes integrals. Chapter 2 deals with Lebesgue measure and integration.
The authors include some famous, and some not so famous, integral inequalities related to Riemann integration. Many of the problems for Lebesgue integration concern convergence theorems and the interchange of limits and integrals. The book closes with a section on Fourier series, with a concentration on Fourier coefficients of functions from particular classes and on basic theorems for convergence of Fourier series.
The book is primarily geared toward students in analysis, as a study aid, for problem-solving seminars, or for tutorials. It is also an excellent resource for instructors who wish to incorporate problems into their lectures. Solutions for the problems are provided in the book.
Undergraduates, graduate students, and instructors interested in analysis.
Table of Contents
Part 1. Problems
Part 2. Solutions