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

这是一个研究项目， 数学、Banach空间理论和概率领域 理论前者与级数的收敛性有关。 经典地，级数的项是函数，但是 在概念上， 是抽象Banach空间中的向量重新专业化， 数列的项可以是随机变量， 研究是概率论的核心。这一点 最近的观点证明是非常有成效的。 更具体地说，塔拉格兰德教授将继续 新组合和等周的引入 概率论中的方法特定目标 更好地理解必要和充分 p-稳定过程样本有界的条件 他还将解决一个著名的公开问题在巴拿赫 与经典空间有关的空间理论 单位区间上的绝对可积函数

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.