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Vietnam Journal of Mathematics 34:2(2006) 179-187

 On Convergence of Vector-Valued Weak Amarts and Pramarts

Dinh Quang Luu

Abstract.  A sequence (X_n) of random elements in Banach space E is called essentially (weakly) tight if and only if for every ε > 0 there exists a (weakly) compact subset K of E such that . The main aim of this note is to give some (weakly) almost sure convergence results for E - valued weak amarts and pramarts in terms of their essential (weak) tightness.

2000 Mathematics Subject Classification: 60G48, 60B11.

Keywords: Banach spaces, a.s. convergence, weak amart and pramart.

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Published by Springer since January 2013