Weekly Calendar
The heart of recent joint work with J"urgen Bliedtner is a technique to simplify the validation of "almost everywhere" limit results in analysis and probability theory. This technique has produced new op- timal limit theorems in both potential theory and measure theory. These optimal results require a consistent choice of where zero limits must oc- cur. Such a consistent choice produces an operator e on sets, where e(A) is the set of points where A is "thick". To understand the possible choices for zeros in the limit theorems, we have had to study the operator e. We have simplified and extended the literature on this operator; it is basic in parts of analysis and topology. After reviewing this work, the talk re- turns to an application of one of the optimal limit theorems: A linear and multiplicative selection of functions from equivalence classes of functions is made so that the value c is taken at every point x where the selected function is approximately equal to c on a set thick at x.