Hyperbolic Measures on Infinite Dimensional Spaces

TL;DR

This paper explores localization and dilation techniques for infinite dimensional alpha-concave measures within locally convex spaces, expanding the understanding of hyperbolic measures in high-dimensional analysis.

Contribution

It introduces new methods for analyzing hyperbolic measures on infinite dimensional spaces, extending Borell's hierarchy.

Findings

Developed localization procedures for alpha-concave measures

Established dilation techniques in infinite dimensional settings

Enhanced theoretical framework for hyperbolic measures

Abstract

Localization and dilation procedures are discussed for infinite dimensional $\alpha$-concave measures on abstract locally convex spaces (following Borell's hierarchy of hyperbolic measures).