I would like your comment (or another suggestions) on the 2 measure theory books for self-study:
- Introduction to measure theory by Terence Tao
- Measures, Integrals and Martingales by René L. Schilling
My goal is to have only necessary foundations (because I don't want to go too deep in the measure theory) to understand the rigorous foundation of probability (to the point of Brownian motion and Ito's calculus) and furthermore, the theoretical foundation of statistics ($i.e$ to understand the rigorous logic behind Maximum Likelihood Estimator or hypothesis testing, monte-carlo simulation).
- Which measure theory book of these 2 books above will serve better for my purpose ?
- Could you suggest me a book (good for self-study) on Probability/statistics which serve my purposes above ?
Thank you very much!