Introduction to Lebesgue Integration
by WWL Chen
This set of notes was mainly written in 1977 while the author was an undergraduate at Imperial College, University of London. Chapters 1 and 3 were first used in lectures given there in 1982 and 1983, while Chapter 2 was added in Sydney in 1996.
The material has been organized in such a way to create a single volume suitable for an introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory.
To read the notes, click the chapters below for connection to the appropriate PDF files.
The material is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, the documents may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners.
Chapter 1: THE REAL NUMBERS AND COUNTABILITY
Chapter 2: THE RIEMANN INTEGRAL
Chapter 4: THE LEBESGUE INTEGRAL
Chapter 5: MONOTONE CONVERGENCE THEOREM
Chapter 6: DOMINATED CONVERGENCE THEOREM
Chapter 7: LEBESGUE INTEGRALS ON UNBOUNDED INTERVALS
Chapter 8: MEASURABLE FUNCTIONS AND MEASURABLE SETS
Chapter 9: CONTINUITY AND DIFFERENTIABILITY OF LEBESGUE INTEGRALS
Chapter 10: DOUBLE LEBESGUE INTEGRALS