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A class of bounds for convex bodies in Hilbert space. (English) Zbl 0776.52003

The author extends to infinite dimension a class of bounds for \(L_ p\) metrics of finite-dimensional convex bodies. A generalization to arbitrary increasing convex functions is done simultaneously.

MSC:

52A41 Convex functions and convex programs in convex geometry
26B25 Convexity of real functions of several variables, generalizations
52A22 Random convex sets and integral geometry (aspects of convex geometry)
60D05 Geometric probability and stochastic geometry
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