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

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Astashkin S., Sukochev F., Zanin D.

Studia Mathematica

2015

tom 230

nr 1

41-57

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 $f ∈ L_{p}$ 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 $f ∈ L_{p}$ whose independent copies span $l_{M}$ in $L_{p}$ is essentially unique.

Ograniczanie wyników

1 Studia Mathematica

1 Astashkin S.

1 Sukochev F.

1 Zanin D.

1 2015

Wyniki wyszukiwania

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