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

 

Lacunary convergence of series in $L_{0}$


Authors: Lech Drewnowski and Iwo Labuda
Journal: Proc. Amer. Math. Soc. 126 (1998), 1655-1659
MSC (1991): Primary 46E30, 40A30, 28A20
MathSciNet review: 1443149
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Abstract: For a finite measure $\lambda $, let $L_{0}(\lambda )$ denote the space of $\lambda $-measurable functions equipped with the topology of convergence in measure. We prove that a series in $L_{0}(\lambda )$ is subseries (or unconditionally) convergent provided each of its lacunary subseries converges.


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Additional Information

Lech Drewnowski
Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60–769 Poznań, Poland
Email: drewlech@math.amu.edu.pl

Iwo Labuda
Affiliation: Department of Mathematics, University of Mississippi, University, Mississippi 38677
Email: mmlabuda@vm.cc.olemiss.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04189-6
PII: S 0002-9939(98)04189-6
Keywords: Space of all measurable functions, subseries convergence in measure, lacunary subseries
Received by editor(s): February 18, 1996
Additional Notes: The final version of this paper was written while the first author held a visiting position in the Department of Mathematics, University of Mississippi, in the Spring Semester of 1996. The first author was also partially supported by the State Committee for Scientific Research (Poland), grant no. 2 P301 003 07.
Communicated by: Dale Alspach
Article copyright: © Copyright 1998 American Mathematical Society