Stochastic approximation properties in Banach spaces

V. P. Fonf, et al. "Stochastic approximation properties in Banach spaces." Studia Mathematica 159.1 (2003): 103-119. <http://eudml.org/doc/284935>.

@article{V2003,
abstract = {We show that a Banach space X has the stochastic approximation property iff it has the stochasic basis property, and these properties are equivalent to the approximation property if X has nontrivial type. If for every Radon probability on X, there is an operator from an $L_\{p\}$ space into X whose range has probability one, then X is a quotient of an $L_\{p\}$ space. This extends a theorem of Sato’s which dealt with the case p = 2. In any infinite-dimensional Banach space X there is a compact set K so that for any Radon probability on X there is an operator range of probability one that does not contain K.},
author = {V. P. Fonf, W. B. Johnson, G. Pisier, D. Preiss},
journal = {Studia Mathematica},
keywords = {measures on Banach spaces; stochastic approximation property},
language = {eng},
number = {1},
pages = {103-119},
title = {Stochastic approximation properties in Banach spaces},
url = {http://eudml.org/doc/284935},
volume = {159},
year = {2003},
}

TY - JOUR
AU - V. P. Fonf
AU - W. B. Johnson
AU - G. Pisier
AU - D. Preiss
TI - Stochastic approximation properties in Banach spaces
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 1
SP - 103
EP - 119
AB - We show that a Banach space X has the stochastic approximation property iff it has the stochasic basis property, and these properties are equivalent to the approximation property if X has nontrivial type. If for every Radon probability on X, there is an operator from an $L_{p}$ space into X whose range has probability one, then X is a quotient of an $L_{p}$ space. This extends a theorem of Sato’s which dealt with the case p = 2. In any infinite-dimensional Banach space X there is a compact set K so that for any Radon probability on X there is an operator range of probability one that does not contain K.
LA - eng
KW - measures on Banach spaces; stochastic approximation property
UR - http://eudml.org/doc/284935
ER -