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A Concentration of Measure Phenomenon on Uniformly Convex Bodies

  • M. Schmuckenschläger
Part of the Operator Theory Advances and Applications book series (OT, volume 77)

Abstract

In his paper [M] B. Maurey gave a very simple proof of the gaussian deviation inequality, based on an inequality of A. Prekopa [Pr] and L. Leindler [L]. Motivated by Talagrand’s isoperimetric inequality for the cube (cf. [T.3]) Maurey defined a property which he called property (τ). He proved that in the gaussian case this property is a consequence of the Prekopa-Leindler inequality. This method can be easily extended to give a concentration of measure phenomenon for a particular measure associated with uniformly convex spaces whose modulus of convexity satisfies a certain condition. In [Pi] G. Pisier proved that this condition can be guaranteed after renorming. Prom this we deduce the concentration of measure result of M. Gromov and V.D. Milman (cf. [G.M.2]) for uniformly convex bodies, whose modulus of convexity satisfies the condition mentioned above.

Keywords

Unit Ball Convex Body Lipschitz Function Convex Space Measurable Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • M. Schmuckenschläger
    • 1
    • 2
  1. 1.Weizmann Institute of ScienceRehovotIsrael
  2. 2.J. Kepler UniversitätLinzAustria

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