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 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 language | English |
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Pages (from-to) | 103-119 |
Number of pages | 17 |
Journal | Studia Mathematica |
Volume | 159 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2003 |
ASJC Scopus subject areas
- General Mathematics