18.125

Real Analysis

Prereqs

• 18.100 - Absolutely necessary.

Textbook

• Stroock - In general good, but hard to follow in some of the longer proofs. Beware of typos.

Comments

Covers measure theory, Lebesgue integration, Lp spaces, and some more advanced topics, including Hilbert spaces and Fourier transforms, Radon-Nikodym derivatives, Lebesgue differentiation theorem, among others. The material covered here forms the foundation of modern analysis and probability theory. It is interesting, but it can be messy and all too easy to get lost in the epsilons.