Abstract:
Convergence almost everywhere of sums of independent lp-valued (1⩽p<∞) random variables is studied. As a corollary, the strong law of large numbers is obtained.
Citation:
Nguyen Zuy Tien, “Some remarks on convergence of sums of independent lp-valued random variables, 1⩽p<+∞”, Teor. Veroyatnost. i Primenen., 21:2 (1976), 395–398; Theory Probab. Appl., 21:2 (1977), 386–388
\Bibitem{Ngu76}
\by Nguyen~Zuy~Tien
\paper Some remarks on convergence of sums of independent $l_p$-valued random variables, $1\le p<+\infty$
\jour Teor. Veroyatnost. i Primenen.
\yr 1976
\vol 21
\issue 2
\pages 395--398
\mathnet{http://mi.mathnet.ru/tvp3357}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=415708}
\zmath{https://zbmath.org/?q=an:0366.60079}
\transl
\jour Theory Probab. Appl.
\yr 1977
\vol 21
\issue 2
\pages 386--388
\crossref{https://doi.org/10.1137/1121044}
Linking options:
https://www.mathnet.ru/eng/tvp3357
https://www.mathnet.ru/eng/tvp/v21/i2/p395
This publication is cited in the following 4 articles:
Dang-Hung-Thang, Nguen-Zuǐ-Tien, “On symmetric stable measures on spaces $l_p$ ($1\le p<+\infty$)”, Theory Probab. Appl., 25:1 (1980), 118–127
Nguyen Duy Tien, “Sur le théorème des trois séries de Kolmogorov et la convergence en moyenne quadratique des martingales dans un espace de Banach”, Theory Probab. Appl., 24:4 (1980), 797–808
I. F. Pinelis, “On the distribution of sums of independent Banach-space-valued random variables”, Theory Probab. Appl., 23:3 (1978), 608–615
V. V. Kvaračheliya, Nguen Zuy Tien, “The central limit theorem and the strong law of large numbers in $l_p\{X\}$-spaces, $1\le p<+\infty$”, Theory Probab. Appl., 21:4 (1977), 780–790