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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 $\Bbb E$ is called essentially (weakly) tight if and only if for every $\varepsilon>0$ there exists a (weakly) compact subset $K$ of $\Bbb E$ such that $\Bbb P(\bigcap\limits_{n\in\Bbb N}[X_n\in K])>1-\varepsilon$. The main aim of this note is to give some (weakly) almost sure convergence results for $\Bbb E$ - 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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