Edwin Hewitt's work in analysis

Ed is well known as a topologist and as an analyst. In fact, much of his work concerned the structure of and analysis on topological algebraic structures like locally compact abelian groups (LCA groups) and topological semigroups. My friend Wis Comfort will report on his work in general topology in an article in a future issue of TopCom. In the early 1950s, Ed turned his attention to various aspects of analysis. One of the most widely referenced results is the Hewitt-Savage Zero-One Law in probability 1955, Theorem 11.3]. It was clear immediately that this was an important result which would appear in most modern probability books. In that paper, they wrote that this result \was commented on by several who saw a prepublication copy of this paper. Blackwell, and Chung and Derman wrote us independently that they had become interested in the following question in connection with forthcoming publications. Is it true that the partial sums of a sequence of identically distributed independent random variables visit an arbitrary Borel set innnitely often with probability either 0 or 1? As they point out, the aarmative answer, which they had already demonstrated in certain cases, is an immediate consequence of Theorem 11.3. Halmos and Doob have shown us direct proofs, both of which make it plain that the theorem is close to and scarcely deeper than the ordinary 0-1 law. These proofs are, with their authors' permission, presented below." The main purpose of this ne paper was, in Ed's own words HF]: \a construction of measures on extreme points of a convex set that is a special case of what later became Choquet theory." Another early paper that Ed was very pleased with was about nitely additive measures and written jointly with K^ osaku Yosida 1952]. Ed so greatly admired Yosida that he insisted that Yosida be the rst-listed author. Ed later decided this was a bad policy, even when he worked with other alphabetically-challenged co-authors whom he greatly admired, like Herbert Zuckerman. Ed's note 1957b] with John Williamson played an important role in my life because it was the rst paper I tried to read and understand.