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

 

Almost everywhere convergence of series in $L^1$


Author: Ciprian Demeter
Journal: Proc. Amer. Math. Soc. 133 (2005), 2319-2326
MSC (2000): Primary 42B20, 28D05, 40A30, 26D15.
Published electronically: March 22, 2005
MathSciNet review: 2138874
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Abstract: We answer positively a question of J. Rosenblatt (1988), proving the existence of a sequence $(c_i)$ with $\sum_{i=1}^{\infty}\vert c_i\vert=\infty$, such that for every dynamical system $(X,\Sigma, m, T)$ and $f\in L^1(X)$, $\sum_{i=1}^{\infty}c_i f(T^ix)$ converges almost everywhere. A similar result is obtained in the real variable context.


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Additional Information

Ciprian Demeter
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095-1555
Email: demeter@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07957-8
PII: S 0002-9939(05)07957-8
Received by editor(s): October 24, 2003
Published electronically: March 22, 2005
Communicated by: Andreas Seeger
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.