I am looking for a very gentle first book on measure theory. I want to acquaint myself with the basic ideas in Measure theory. Briefly, my background is as follows.
I am self-learning basic probability theory through a couple of books:
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Introduction to Probability theory and its applications, Volume I – William Feller. (Currently reading Chapter X. Law of Large Numbers).
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Probability and Random Processes – Grimmett and Stirzaker (Currently studying Chapter II. Random variables and distribution functions).
I am also learning Real Analysis (at the level of Baby Rudin) through the book:
- Understanding Analysis, Stephen Abbott. (Currently reading chapter II on sequences and series).
One of the books I have in mind, is Sheldon Axler's book on measure theory (it's modern). Do you think I can jump into it anyway, given my current background? Also, any video playlists(lectures) are welcome.
Best Answer
Check out A First Look at Rigorous Probability Theory by Rosenthal. The first five chapters, in particular, seem like exactly what you're looking for: a very gentle introduction to the basics of measure theory with an eye toward probability.