Bounded multiplier convergence in measure of random vector series
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- by C. Ryll-Nardzewski and W. A. Woyczyński PDF
- Proc. Amer. Math. Soc. 53 (1975), 96-98 Request permission
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.References
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B. Maurey and G. Pisier, Un théorème d’extrapolation et ses consequences, C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A39-A42.
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.
- Stefan Rolewicz, Metric linear spaces, 2nd ed., PWN—Polish Scientific Publishers, Warsaw; D. Reidel Publishing Co., Dordrecht, 1984. MR 802450
- 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 215329
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 96-98
- MSC: Primary 60B10; Secondary 46E40
- DOI: https://doi.org/10.1090/S0002-9939-1975-0385960-5
- MathSciNet review: 0385960