This course consists of two (at times closely interrelated) parts:
Part I: Measure and integration
Part II: Linear operators, mostly on Hilbert spaces
Literature
- "Spaces -- An introduction to Real Analysis", 1st edition (AMS, 2017), by Tom L. Lindstrøm. Here is a list of known misprints in "Spaces".
- "Notes on Elementary Linear Analysis" by Erik Bédos. These notes can be downloaded here.
The curriculum will consist of chapter 7 (except section 7.7) and chapter 8 (except sections 8.6-8.8) in Spaces plus the notes on linear analysis. If time admits, we shall also take a brief look at sections 8.7-8.8 in Spaces. These sections really belong to the next course MAT4410, but the basic ideas are useful to know about.
Alternative literature
It can often be helpful to look at other presentations of the curriculum. Here are some possibilities:
"A course in real analysis" by John McDonald and Neil Weiss, 2nd edition (used as the textbook for the measure theory part of the course until 2018).
"Linear Functional Analysis" (2nd edition) by Bryan P. Rynne and Martin A. Youngson, Springer Undergraduate Mathematics Series. (used as the textbook for the functional analysis part of the course until 2017).
"Topics in Real and Functional Analysis" by G. Teschl. These lecture notes were used for the early versions of the course. They are freely downloadable from the author's homepage, but are rather tersely written for a course on this level.