Measure and Integration Theory

A truly remarkable introductory text on abstract measure theory. The topics and results are well-organized. The author writes with precision and rarely skips steps. I've gone through the book and carefully filled in the gaps in detail, and that took 20 pages. This may sound like quite a lot, but it really isn't. The last chapter does draw upon a substantial number of results from introductory general topology. When I typed up complete notes for this background material (including detailed proofs of Zorn's Lemma and the Tychonoff Theorem), it took me another 24 pages. It should be said that a lot of the stuff in that final chapter goes well beyond what is typically covered in a one-semester measure theory course. For example, it includes show more the Portmanteau Theorem and Prohorov's Theorem, which are usually considered to be results of probability theory. show less