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, 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.
Author(s): W. J. Kaczor, M. T. Nowak
Series: Student Mathematical Library 21
Edition: 1
Publisher: American Mathematical Society
Year: 2003
Language: English
Pages: 369
Tags: Mathematical Analysis
Cover
Title
Copyright
Contents
Preface
Part 1. Problems
Chapter 1. The Riemann-Stieltjes Integral
§1.1. Properties of the Riemann-Stieltjes Integral
§1.2. Functions of Bounded Variation
§1.3. Further Properties of the Riemann-Stieltjes Integral
§1.4. Proper Integrals
§1.5. Improper Integrals
§1.6. Integral Inequalities
§1.7. Jordan Measure
Chapter 2. The Lebesgue Integral
§2.1. Lebesgue Measure on the Real Line
§2.2. Lebesgue Measurable Functions
§2.3. Lebesgue Integration
§2.4. Absolute Continuity, Differentiation and Integration
§2.5. Fourier Series
Part 2. Solutions
Chapter 1. The Riemann-Stieltjes Integral
§1.1. Properties of the Riemann-Stieltjes Integral
§1.2. Functions of Bounded Variation
§1.3. Further Properties of the Riemann-Stieltjes Integral
§1.4. Proper Integrals
§1.5. Improper Integrals
§1.6. Integral Inequalities
§1.7. Jordan Measure
Chapter 2. The Lebesgue Integral
§2.1. Lebesgue Measure on the Real Line
§2.2. Lebesgue Measurable Functions
§2.3. Lebesgue Integration
§2.4. Absolute Continuity, Differentiation and Integration
§2.5. Fourier Series
Bibliography -Books
Index
A
B
C
D
E
F
H
I
J
L
M
O
P
R
S
T
U
V
W
Y
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