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

S. V. Astashkin
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Abstract

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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S. V. Astashkin. 2000-08-07. Selection of subsystems of random variables equivalent in distribution to the Rademacher system. https://arxiv.org/abs/math/0008053

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