Stochastic approximation properties in Banach spaces

V. P. Fonf, W. B. Johnson, G. Pisier, D. Preiss

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Pages (from-to)103-119
Number of pages17
JournalStudia Mathematica
Issue number1
StatePublished - 1 Jan 2003

ASJC Scopus subject areas

  • General Mathematics


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