Convex bodies and norms associated to convex measures

• 成果类型: Article
• 署名作者: Bobkov, Sergey G.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0209-7
• 发表日期: 2010
• 页码: 303-332
• 关键词: concave functions; brunn-minkowski; inequalities

摘要

Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball's relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions, satisfying convexity conditions of the Brunn-Minkowski type.