Lebesgue Integration 0486789772, 9780486789774

This concise introduction to Lebesgue integration is geared toward advanced undergraduate math majors and may be read by

351 110 3MB

English Pages 123 [124] Year 2014

Table of contents :
Cover
Title Page
Copyright Page
Preface
Table of Contents
Chapter 1. Sets and Functions
1.1. Generalities
1.2. Countable and Uncountable Sets
1.3. Sets in R^n
1.4. Compactness
1.5. Functions
Chapter 2. Lebesgue Measure
2.1. Preliminaries
2.2. The Class
2.3. Measurable Sets
2.4. Sets of Measure Zero
2.5. Borel Sets and Nonmeasurable Sets
Chapter 3. The Integral I
3.1. Definition
3.2. Elementary Properties
3.3. Measurable Functions
3.4. Complex and Vector Functions
3.5. Other Definitions of the Integral
Chapter 4. The Integral II
4.1. Convergence Theorems
4.2. Fubinis Theorems
4.3. Approximations to Integrable Functions
4.4. The L p Spaces
4.5. Convergence in Mean
4.6. Fourier Theory
Chapter 5. Calculus
5.1. Change of Variables
5.2. Differentiation of Integrals
5.3. Integration of Derivatives
5.4. Integration by Parts
Chapter 6. More General Measures
6.1. Borel Measures
6.2. Signed Measures and Complex Measures
6.3. Absolute Continuity
6.4 Measures, Functions, and Functionals
6.5 Norms, Fourier Transforms, Convolution Products
Index

Lebesgue Integration
0486789772, 9780486789774

Author / Uploaded
J. H. Williamson

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