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Studia Mathematica

2003 | 159 | 1 | 103-119
Tytuł artykułu

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 $L_{p}$ 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.
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Numer
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103-119
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
• Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
autor
• Department of Mathematics, Texas A&M University, Department of Mathematics, College Station, TX 77843, U.S.A.
autor
• Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A.
• Equipe d'Analyse, Case 186, Université Paris VI, 75252 Paris, Cedex 05, France
autor
• Department of Mathematics, University College London, London, Great Britain
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