Preface I am an analyst. I use measure theory almost every day of my life. Yet for most of my career I have disliked it as a stand-alone subject and avoided teaching it. I taught a two-semester course on the subject during the second year after I earned my doctorate and never again until Fall 2010. Then I decided to teach our year long course that had a semester of measure theory followed by a semester of functional analysis, a course designed to prepare first-year graduate students for the PhD Qualifying exam. The spring before the course was to begin, I began to think about how I would present the material. In the process I discovered that with an approach different from what I was used to, there is a certain elegance in the subject. It seems to me that the customary presentation of basic measure theory has changed little since I took it as a first-year graduate student. In addi- tion, when I wrote my book on functional analysis [8], it was premised on students having completed a year long course in measure theory, something that seldom happens now. For these two reasons and because of my newly found appreciation of measure theory, I made the decision that I would write a book. For this project I resolved to look at this subject with fresh eyes, simplifying and streamlining the measure theory, and formulating the func- tional analysis so it depends only on the measure theory appearing in the same book. This would make for a self-contained treatment of these sub- jects at the level and depth appropriate for my audience. This book is the culmination of my effort. What did I formerly find unpleasant about measure theory? It strikes me that most courses on measure theory place too much emphasis on topics I never again encountered as a working analyst. Some of these are natural enough within the framework of measure theory, but they just don’t arise xi
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