Mathematical Sciences: Applications of Nonstandard Analysis to Measure Theory, Potential Theory & Related Topics

数学科学：非标准分析在测度论、势论中的应用

• 批准号: 9201494
• 负责人: Peter Loeb
• 金额: $ 7.25万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201494&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Nonstandard; Analysis

Loeb will continue his work in applying nonstandard models to measure theory, potential theory, and stochastic processes. This approach uses measure spaces defined on nonstandard point sets. These spaces make finite combinatorial methods available in research on infinite probability spaces. Loeb will combine this measure theory with the theory of nonstandard hulls. He also will continue his work on representing measures and ideal boundaries in potential theory. This research project is in the area of nonstandard analysis. This subject arises from the attempt to develop the standard topics of analysis, including integration and differentiation, based on a nonstandard model for the real numbers. In the nonstandard model, one has the notion of "infinitely small" numbers which formalize the intuitive notions behind the concept of limit. This formal construct often leads to greater combinatorial efficiency.

Loeb将继续他的工作，应用非标准模型 测量理论、势理论和随机过程。 这种方法使用定义在非标准点上的测度空间 集. 这些空间使有限组合方法可用 无限概率空间的研究。 勒布将联合收割机 该测量理论与非标准船体理论相结合。 他 也将继续他的工作，代表措施和理想 潜在理论的边界 本研究项目属于非标准化领域 分析. 这一主题产生于试图发展 标准分析主题，包括集成和 微分，基于真实的非标准模型 号码 在非标准模型中，人们有这样的概念： “无穷小”的数字形式化的直观概念 在极限概念的背后。 这种形式上的结构往往导致 提高组合效率。