Getting Started with Measure Theory

Last year, I managed to successfully finish Metric Spaces, Basic Topology and other Analysis topics. Starting from the next semester I’ll be learning more pure mathematical topics, like Functional Analysis, Combinatorics and more. The plan is to lead myself to Combinatorics by majoring Functional Analysis and Topology. But before all those, I’ll be studying measure theory and probability this July – August. Probability theory is not so important as is Measure Theory. This post discusses a rough plan of how should I (& you) begin the study of Measure theory by using great free internet resources. .

This YouTube playlist , compiled by Sam Kolahgar might be the best visual guide for me through the learning period. It has several amazing videos with excellent learning material. The most essential text-guide for Measure Theory will be this pdf file which can be downloaded from Terence Tao’s blog. It is, actually a rough draft copy of his amazing Measure Theory book but enough to introduce basic things. There are also other Measure Theory, Functional Analysis, Metric Space and Real Analysis texts which contain enough material to be read and understood.

More Learning Resources

• Lectures on Measure Theory and Probability
by H. R. Pitt, TIFR, Mumbai.
Brief but very useful chapters on both the Measure Theory and Probability$[Download 540 kB] • Measure Theory Notes by John Hunter Notes on Measure Theory. Easy to grasp. :)$
• Lecture Notes in Measure Theory
by Chister Borell
A bit complex for beginners.$[Download 717 kB] • Lecture Notes in Measure Theory and Functional Analysis by P. Cannarsa & T. D’Aprile Excellent. :)$
• Measure Theory and Integration
by  D. H. Sattinger