Syllabus:

1. Refresher on topology (open sets, compactness, connectedness,
continuity, metric spaces), refresher on Riemann integration.

2. Measure theory: abstract measure spaces, outer measure,
Caratheodory theorem, Radon-Nikodym theorem, Lebesgue integration,
convergence theorems.

3. Measures invariant under group action, Haar measure

4. L^p spaces, Hilbert spaces, Banach spaces, Fourier transforms (time
permitting).

5. Other topics of interest if time permits.

Textbook (available online):

Royden-Fitzpatrick: Real Analysis

References (available online):
1. Rudin: Principles of Mathematical Analysis

2. Munkres: Topology

3. Rudin: Real and Complex Analysis

4. Halmos: Measure theory.

5. Rudin: Functional Analysis