Foundations of Modern Analysis

If you are not already very familiar with the material, this is one of those books where you read a page, mentally process it, wait for the mental light bulb to go off and then read the next page. The material is very condensed, for example the first third of page 46 is the conclusion of the lengthy proof of a lemma and the remainder consists of four definitions, all of which define specific characteristics of integration. There are problems at the end of most sections but no solutions are included. There are six chapters and the titles are: *) Measure theory *) Integration *) Metric spaces *) Elements of functional analysis in Banach spaces *) Completely continuous operators *) Hilbert spaces and spectral theory From these titles, it is easy to see the breadth of the coverage. If you are looking for a book for self-study, this is almost certainly not for you. It is a book that would serve as an effective rapid refresher or as a textbook in graduate level analysis where there is great opportunity for supplemental explanations.