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Teor. Veroyatnost. i Primenen., 1970, Volume 15, Issue 2, Pages 351–357 (Mi tvp1838)  

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 $L$.

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

Bibliographic databases:

Received: 28.10.1968

Citation: D. Kh. Mushtari, “On almost sure convergence in linear spaces of random variables”, Teor. Veroyatnost. i Primenen., 15:2 (1970), 351–357; Theory Probab. Appl., 15:2 (1970), 337–342

Citation in format AMSBIB
\Bibitem{Mus70}
\by D.~Kh.~Mushtari
\paper On almost sure convergence in linear spaces of random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1970
\vol 15
\issue 2
\pages 351--357
\mathnet{http://mi.mathnet.ru/tvp1838}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=279848}
\zmath{https://zbmath.org/?q=an:0217.49701}
\transl
\jour Theory Probab. Appl.
\yr 1970
\vol 15
\issue 2
\pages 337--342
\crossref{https://doi.org/10.1137/1115041}


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