Math 541. Real Analysis II

Textbooks used in past semesters:

• Real Analysis, Modern Techniques and Their Applications, by G.B. Folland 2nd Edition, John Wiley & Sons
• A Course in Functional Analysis by J.B.Conway, 2nd Edition, Springer-Verlag
• Introduction to Modern Analysis by Shmuel Kantorovitz, Graduate Text #8, Oxford University Press.

1. General measure and integration theory, including product measures, Fubini theorem, signed measures, Hahn decomposition theorem, and Lebesgue-Radon-Nikodym theorem.

2. An introduction to functional analysis, including examples of Banach spaces, Hahn--Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness, weak and weak* topologies, Alaoglu's theorem and Krein-Milman theorem (optional).

3. Optional topics, such as bounded and compact operators on Banach spaces and Hilbert spaces; applications to Fourier analysis, harmonic analysis or the theory of Sobolev spaces and distributions.