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Proceedings of the American Mathematical Society

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Bounded multiplier convergence in measure of random vector series


Authors: C. Ryll-Nardzewski and W. A. Woyczyński
Journal: Proc. Amer. Math. Soc. 53 (1975), 96-98
MSC: Primary 60B10; Secondary 46E40
MathSciNet review: 0385960
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Abstract: If the series $ \Sigma {f_i}$ of random vectors with values in a Banach space converges unconditionally in measure, then, for each $ ({\lambda _i})\epsilon {l^\infty }$, the series $ \Sigma {\lambda _i}{f_i}$ also converges unconditionally in measure.


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  • [1] B. Maurey and G. Pisier, Un théorème d'extrapolation et ses consequences, C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A39-A42.
  • [2] K. Musial, C. Ryll-Nardzewski and W. A. Woyczyński, Convergence presque surs des séries aléatoires vectorielles à multiplicateur bornée, C. R. Acad. Sci. Paris Sér. A-B 279 (1974), A225-A228.
  • [3] Stefan Rolewicz, Metric linear spaces, 2nd ed., Mathematics and its Applications (East European Series), vol. 20, D. Reidel Publishing Co., Dordrecht; PWN—Polish Scientific Publishers, Warsaw, 1985. MR 808176
  • [4] K. Urbanik and W. A. Woyczyński, A random integral and Orlicz spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 161–169 (English, with Russian summary). MR 0215329

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0385960-5
Keywords: Unconditional convergence, bounded multiplier, random vector
Article copyright: © Copyright 1975 American Mathematical Society