Probability Surveys

Hyperbolic measures on infinite dimensional spaces

Sergey G. Bobkov and James Melbourne

Full-text: Open access

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).

Article information

Source
Probab. Surveys, Volume 13 (2016), 57-88.

Dates
Received: May 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ps/1465321421

Digital Object Identifier
doi:10.1214/14-PS238

Mathematical Reviews number (MathSciNet)
MR3511344

Zentralblatt MATH identifier
1342.60006

Subjects
Primary: 60B11: Probability theory on linear topological spaces [See also 28C20] 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 60F10: Large deviations

Keywords
Hyperbolic (convex) measures dimension localization dilation of sets

Citation

Bobkov, Sergey G.; Melbourne, James. Hyperbolic measures on infinite dimensional spaces. Probab. Surveys 13 (2016), 57--88. doi:10.1214/14-PS238. https://projecteuclid.org/euclid.ps/1465321421


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References

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