This course consists of two (at times closely interrelated) parts:
Part I: Measure and integration
Part II: Bounded linear operators on Banach spaces and Hilbert spaces.
- "A course in real analysis" by John McDonald and Neil Weiss, 2nd edition. (for part one)
- "Linear Functional Analysis" (2nd edition) by Bryan P. Rynne and Martin A. Youngson, Springer Undergraduate Mathematics Series. (for part two)
The following sections from McDonald and Weiss:
6.1, 6.3, and 6.4,
13.1, 13.2, and 13.4 up to and including Theorem 13.11.
The following sections from Rynne-Youngson:
5.1 only Theorem 5.2.
6.1, 6.2, 6.3 up to and including Theorem 6.39, and 6.4 up to and including Lemma 6.57.