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

S. Astashkin, F. Sukochev, and D. Zanin. "On uniqueness of distribution of a random variable whose independent copies span a subspace in $L_{p}$." Studia Mathematica 230.1 (2015): 41-57. <http://eudml.org/doc/285894>.

@article{S2015,
abstract = {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.},
author = {S. Astashkin, F. Sukochev, D. Zanin},
journal = {Studia Mathematica},
keywords = {lp-space; Orlicz sequence space; independent random variables; p-convex function; q-concave function; subspaces},
language = {eng},
number = {1},
pages = {41-57},
title = {On uniqueness of distribution of a random variable whose independent copies span a subspace in $L_\{p\}$},
url = {http://eudml.org/doc/285894},
volume = {230},
year = {2015},
}

TY - JOUR
AU - S. Astashkin
AU - F. Sukochev
AU - D. Zanin
TI - On uniqueness of distribution of a random variable whose independent copies span a subspace in $L_{p}$
JO - Studia Mathematica
PY - 2015
VL - 230
IS - 1
SP - 41
EP - 57
AB - 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.
LA - eng
KW - lp-space; Orlicz sequence space; independent random variables; p-convex function; q-concave function; subspaces
UR - http://eudml.org/doc/285894
ER -