Mathematical Sciences: Descriptive Set Theoretic and Probabilistic Methods in Topology and Analysis

数学科学：拓扑与分析中的描述集理论和概率方法

• 批准号: 8803361
• 负责人: R. Daniel Mauldin
• 金额: $ 3.4万
• 依托单位: University of North Texas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803361&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Descriptive; Set; Theoretic

Mauldin plans to investigate the random generation of homeomorphisms of the circle and other objects. Computer studies are useful here. He plans to develop further methods of calculating and estimating Hausdorff dimension and measure, particularly within the context of dynamical systems and random geometric instructions. This includes an analysis of the Weierstrass nowhere differentiable functions. He plans to characterize those continua which have sigma-finite linear measure in some metric. He plans to develop further techniques in descriptive set theory with applications to orthogonal transition kernels (positive operators) and 1-1 selections in mind.

莫尔丁计划研究随机生成的 圆和其他物体的同胚。 计算机研究 在这里很有用。 他计划进一步开发 计算和估计Hausdorff维数和测度， 特别是在动态系统和随机系统的背景下， 几何指令 其中包括对 Weierstrass无处可微函数。 他计划 刻画了具有σ-有限线性的连续统 用某种度量衡来衡量。 他计划进一步发展技术 在描述集合论中， 转换核（正算子）和1-1选择 主意了