On uniqueness of distribution of a random variable whose independent copies span a subspace in $L_{p}$

S. Astashkin; F. Sukochev; D. Zanin

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

L_{p}

S. Astashkin ; F. Sukochev ; D. Zanin

Studia Mathematica, Tome 231 (2015), p. 41-57 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let 1 ≤ 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 $f \in L_{p}$ 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.

Publié le : 2015-01-01

Zbl 06545399

EUDML-ID : urn:eudml:doc:285894

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     title = {On uniqueness of distribution of a random variable whose independent copies span a subspace in $L\_{p}$
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     year = {2015},
     pages = {41-57},
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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 231 (2015) pp. 41-57. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8089-1-2016/