Selection of subsystems of random variables equivalent in distribution to the Rademacher system

Details Selection of subsystems of random variables equivalent in distribution to the Rademacher system Selection of subsystems of random variables equivalent in distribution to the Rademacher system

2000-08-07

arxiv.org/abs/math/0008053v1

Matemat. Sbornik, V.191, No.6 (2000), 3-30 (in Russian)

Mathematics

Functional Analysis

26 pages

Scientific paper

We present necessary and sufficient conditions on systems of random variables for them to possess a lacunary subsystem equivalent in distribution to the Rademacher system on the segment [0,1]. In particular, every uniformly bounded orthonormal system has this property. Furthermore, an arbitrary finite uniformly bounded orthonormal set of N functions contains a subset of "logarithmic" density equivalent in distribution to the corresponding set of Rademacher functions, with a constant independent of N. A connection between the tail distribution and the L_p-norms of polynomials with respect to systems of random variables exploited. We use also these results to study K-closed representability of some Banach couples.

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