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

数学科学：测度论在概率和 Banach 空间中的应用

• 批准号: 8801180
• 负责人: Michel Talagrand
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801180&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Application; Measure; Theory

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.

这是一个研究两个数学领域的项目，巴拿赫空间理论和概率论。前者与级数的收敛性有关。经典地，级数的项是函数，但是把它们简单地看作抽象巴拿赫空间中的向量有一个概念上的优势。再特殊化，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卓有成效的。更具体地说，塔拉格兰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稳定过程的样本有界性的充分必要条件。他还将解决巴拿赫空间理论中一个著名的开放问题，该问题与单位区间上绝对可积函数的经典空间有关。