This file describes the construction of an abstract integral. It follows Walter Rudin's excellent treatment in his book, " Real and Complex Analysis". Abstract Integration
This is a summary of topics covered in the course "Measure and Integral". Thanks are due to Chris Ridler-Rowe who created the original. Summary
Elementary Exercises on topology of the Real Line. The properties of compact sets are vital for proving properties of Lebesgues measure. These exercises cover the necessary ideas. Topology Exercises.
A discussion of extending the idea of Measurable Functions. Probably best read after a basic course in Measure and Integration. Measurable Functions
The following links are for the various chapters of the course MP3/4, Lebesgues Integral. This way of developing the Integral is due to Young and deliberately avoids the slicker treatments which have more hindsight. These are working notes, not canonical, and have an average number of typos and a few errors - see if you can find some!Chapter 1 of MP3 , Chapter 2 of MP3, Chapter 3 of MP3, Chapter 4 of MP3, Chapter 5 of MP3, Chapter 6 of MP3, Chapter 7 of MP3, Chapter 8 of MP3, Chapter 9 of MP3, Chapter 10 of MP3, Chapter 11 of MP3, Chapter 12 of MP3, Chapter 13 of MP3.