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

Volume 230 / 2015

S. Astashkin, F. Sukochev, D. Zanin Studia Mathematica 230 (2015), 41-57 MSC: 46E30, 46B20, 46B09. DOI: 10.4064/sm8089-1-2016 Published online: 21 January 2016

Abstract

Let $1\leq p \lt 2$ 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 $f\in L_p$ spans in $L_p$ a subspace isomorphic to some Orlicz sequence space $l_M$. We give precise connections between $M$ and $f$ and establish conditions under which the distribution of a random variable $f\in L_p$ whose independent copies span $l_M$ in $L_p$ is essentially unique.

Authors

  • S. AstashkinSamara State University
    Pavlova 1
    443011, Samara, Russia
    and
    Samara State Aerospace University (SSAU)
    Moskovskoye shosse 34
    443086, Samara, Russia
    e-mail
  • F. SukochevSchool of Mathematics and Statistics
    University of New South Wales
    Sydney, 2052, Australia
    e-mail
  • D. ZaninSchool of Mathematics and Statistics
    University of New South Wales
    Sydney, 2052, Australia
    e-mail

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