期刊
EUROPEAN JOURNAL OF MATHEMATICS
卷 9, 期 1, 页码 -出版社
SPRINGER INT PUBL AG
DOI: 10.1007/s40879-023-00607-2
关键词
Concentration of measure; Compact Lie groups; Riemann geometry; Metric measurable spaces; Topological dynamics
类别
This paper examines the concentration of measure in metric-measurable (mm)-spaces, particularly focusing on the concentration locus of a flag sequence of such spaces. The trajectory of the concentration locus is illustrated through examples of infinite group action on infinite dimensional compact and non-compact manifolds. Furthermore, the paper discusses the significance of concentration of measure in gravitational effects, providing applications in physics.
We study the concentration of measure in metric-measurable (mm)-spaces. We define the notion of concentration locus of a flag sequence of metric-measurable (mm)-spaces. Some examples of infinite group action on an infinite dimensional compact and non-compact manifold show the role played by the trajectory of concentration locus. We also provide some applications in physics, which emphasize the role of concentration of measure in gravitational effects.
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