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Stochastic approximation properties in Banach spaces

V. P. Fonf, W. B. Johnson, G. Pisier, D. Preiss (2003)

Studia Mathematica

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...

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