English

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

Functional Analysis 2014-06-20 v1

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.

Keywords

Cite

@article{arxiv.1406.4950,
  title  = {On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p},
  author = {S. Astashkin and F. Sukochev and D. Zanin},
  journal= {arXiv preprint arXiv:1406.4950},
  year   = {2014}
}

Comments

14 pages, submitted