Mathematical Sciences: Application of Measure Theory to Probability and Banach Spaces

这是一个研究两个数学领域--Banach空间理论和概率理论--的项目。前者与级数的收敛有关。传统上，该系列的术语是函数，但将它们简单地视为抽象Banach空间中的矢量有一个概念上的优势。再具体地说，序列的项可以是随机变量，其研究是概率论的核心。这种观点最近被证明是非常富有成效的。更具体地说，塔拉格兰德教授将继续介绍概率论中新的组合和等周方法。一个特殊的目标是更好地理解p-稳定过程样本有界的充要条件。他还将解决Banach空间理论中一个著名的公开问题，该问题与单位区间上绝对可积函数的经典空间有关。

This is a project for research at the interface of two areas of mathematics, Banach space theory and probability theory. The former has to do with the convergence of series. Classically, the terms of the series are functions, but there is a conceptual advantage in taking them simply to be vectors in an abstract Banach space. Respecializing, the terms of the series can be random variables, whose study is at the heart of probability theory. This point of view has lately turned out to be very fruitful. More specifically, Professor Talagrand will continue the introduction of new combinatorial and isoperimetric methods in probability theory. A particular objective is better understanding of necessary and sufficient conditions for sample boundedness of p-stable processes. He will also tackle a famous open problem in Banach space theory having to do with the classical space of absolutely integrable functions on the unit interval.