Wellcome to MAT 4410 ! …
Wellcome to MAT 4410 !
The course will be given for the first time this fall. We shall indicate two different sources to the course contents:
1) The book "Real Analysis", by G. B. Folland will cover virtually everything we shall need (and much, much more). Of particular interest to us are
Chap. 2 (§§ 4 and 5) Modes of Convergence, Product Measures.
Chap. 3 (§§ 1-3) Decomposition of measures.
Chap. 6 (§§ 1 and 2) L^p duality, Riesz' Representation Theorem.
Chap. 5 (§§ 2 and 3) Banach spaces and the theorems on open mapping, closed graph, uniform boundedness, and Hahn-Banach.
2) "Topics in Real and Functional Analysis" by G. Teschl will also cover the course, when supplemented by "An Introduction to Measure and Integration" by I. K. Rana. In particular, Chap. 4, 7, 8, 9, and 10 of Teschl's book together with 7.1-7.4 (product measures, Tonelli-Fubini), 8.2-8.3 (modes of convergence), and 9.1 (conditional expectations) in the book of Rana should be sufficient.
The book of Teschl is available for free on the net here
We strongly recommend that you download Teschl's book. Many of the exercises will be taken from that source.