measure theory

My work has become much more technical that I am used to, so I thought it would be good to take some notes on basic measure and probability theory in anticipation of working through several theoretical papers. In this series of posts, I’ll be working through Axler’s Measure, Integration & Real Analysis. I’ll supplement with Tao’s An Introduction to Measure Theory and Durrett’s Probability: Theory and Examples as well as some definitions/ideas from Wikipedia.

Note: Not all of the proofs are finished/included. I am hoping to find the time to return to this post and complete them.