Preface There are a myriad of books about probability theory already on the mar- ket. Nonetheless, a few years ago Sergei Gelfand asked if I would write a probability theory book for advanced undergraduate and beginning gradu- ate students who are interested in mathematics. He had in mind an updated version of the first volume of William Feller’s renowned An Introduction to Probability Theory and Its Applications [3]. Had I been capable of doing so, I would have loved to oblige, but, unfortunately, I am neither the math- ematician that Feller was nor have I his vast reservoir of experience with applications. Thus, shortly after I started the project, I realized that I would not be able to produce the book that Gelfand wanted. In addition, I learned that there already exists a superb replacement for Feller’s book. Namely, for those who enjoy combinatorics and want to see how probability theory can be used to obtain combinatorial results, it is hard to imagine a better book than N. Alon and J. H. Spencer’s The Probabilistic Method [1]. For these reasons, I have written instead a book that is a much more conventional introduction to the ideas and techniques of modern probabil- ity theory. I have already authored such a book, Probability Theory, An Analytic View [9], but that book makes demands on the reader that this one does not. In particular, that book assumes a solid grounding in analy- sis, especially Lebesgue’s theory of integration. In the hope that it will be appropriate for students who lack that background, I have made this one much more self-contained and developed the measure theory that it uses. Chapter 1 contains my attempt to explain the basic concepts in proba- bility theory unencumbered by measure-theoretic technicalities. After intro- ducing the terminology, I devote the rest of the chapter to probability theory on finite and countable sample spaces. In large part because I am such a ix
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