A class of bounds for convex bodies in Hilbert space |
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Authors: | Richard A Vitale |
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Institution: | (1) Department of Statistics, University of Connecticut, 06269-3120 Storrs, CT, USA |
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Abstract: | We extend to infinite dimensions a class of bounds forL
p metrics of finite-dimensional convex bodies. A generalization to arbitrary increasing convex functions is done simultaneously. The main tool is the use of Gaussian measure to effect a normalization for varying dimension. At a point in the proof we also invoke a strong law of large numbers for random sets to produce a rotational averaging.Supported in part by ONR Grant N0014-90-J-1641 and NSF Grant DMS-9002665. |
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Keywords: | Primary: 52A41 secondary: 26B25 26E25 52A05 52A22 52A27 52A39 60D05 |
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