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arXiv · 1406.4950

On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p

S. Astashkin·F. Sukochev·D. Zanin
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Abstract

Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace isomorphic to some Orlicz sequence space l_M. We present precise connections between M and f and establish conditions under which the distribution of a random variable f whose independent copies span l_M in L_p is essentially unique.

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S. Astashkin, F. Sukochev, D. Zanin. 2014-06-19. On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p. https://arxiv.org/abs/1406.4950

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