Geodesic
On uniqueness of distribution of a random variable whose independent copies span a subspace in $L_p$
S. Astashkin 1   ; F. Sukochev 2   ; D. Zanin 2
1 Samara State University Pavlova 1 443011, Samara, Russia and Samara State Aerospace University (SSAU) Moskovskoye shosse 34 443086, Samara, Russia
2 School of Mathematics and Statistics University of New South Wales Sydney, 2052, Australia
Studia Mathematica, Tome 230 (2015) no. 1, pp. 41-57 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm8089-1-2016
Keywords: leq p classical p space classes p integrable functions known sequence independent copies mean zero random variable spans subspace isomorphic orlicz sequence space precise connections between and establish conditions under which distribution random variable whose independent copies span essentially unique

S. Astashkin  1   ; F. Sukochev  2   ; D. Zanin  2

1 Samara State University Pavlova 1 443011, Samara, Russia and Samara State Aerospace University (SSAU) Moskovskoye shosse 34 443086, Samara, Russia
2 School of Mathematics and Statistics University of New South Wales Sydney, 2052, Australia 
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S. Astashkin; F. Sukochev; D. Zanin. On uniqueness of distribution of a random variable whose independent copies span a subspace in $L_p$. Studia Mathematica, Tome 230 (2015) no. 1, pp. 41-57. doi: 10.4064/sm8089-1-2016

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