Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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 (88i:46004b)
  • [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 (35 #6170)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60B10, 46E40

Retrieve articles in all journals with MSC: 60B10, 46E40

Additional Information

PII: S 0002-9939(1975)0385960-5
Keywords: Unconditional convergence, bounded multiplier, random vector
Article copyright: © Copyright 1975 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia