I want to self-study basic probability theory in a rigorous way from the Springer book - Probability essentials by Jean Jacod, Philip Protter. I have taken courses in
- Calculus : Worked through Differential Calculus - N. Piskunov.
- Linear Algebra : Worked through the first six chapters of Linear Algebra done right - Sheldon Axler.
I have no background in Analysis yet. I have only started reading Tao's book.
- What would be the pre-requisites for self-studying probability theory, and can these be picked up along the way?
- Any recommendations for a great video lecture series that covers the subject material.
P.S. I have done some leisure reading and problem solving of volume I of Feller.
Cheers!
Quasar
Probability theory depends heavily on measure theory. After you finish Tao's book, you may want to take a look at my new book Measure, Integration & Real Analysis, whose electronic version is legally available for free at https://link.springer.com/content/pdf/10.1007%2F978-3-030-33143-6.pdf. The last chapter of this book gives a brief introduction to measure-theory-based probability, but for an in-depth treatment of probability you should look elsewhere after learning measure theory.