This article is cited in 11 papers

Short Communications

On almost sure convergence in linear spaces of random variables

D. Kh. Mushtari

Kazan'

Abstract: In this paper, almost sure convergence in a linear space $L$ of random variables with values in a normed space $\mathfrak X$ is considered. In case when $\mathfrak X=R$, it is shown that the necessary and sufficient condition for convergence in measure and a.s. convergence to coincide is nuclearity of $L$.

Received: 28.10.1968

 English version: Theory of Probability and its Applications, 1970, 15:2, 337–342

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