Stochastic approximation properties in Banach spaces
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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 Lp space into X whose range has probability one, then X is a quotient of an Lp 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 list (cited authors)
Fonf, V. P., Johnson, W. B., Pisier, G., & Preiss, D.
complete list of authors
Fonf, VP||Johnson, WB||Pisier, G||Preiss, D