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

 

An extension of a result by Talalyan on the representation of measurable functions by Schauder bases


Author: Ben-Ami Braun
Journal: Proc. Amer. Math. Soc. 34 (1972), 440-446
MSC: Primary 46E30; Secondary 28A20
MathSciNet review: 0295070
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Abstract: We define a class of Banach spaces which in particular include the $ {L^p},1 \leqq p < \infty $, and the separable Orlicz spaces. We show that an arbitrary measurable function can be represented by a series of any Schauder basis chosen from that class of Banach spaces.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0295070-0
PII: S 0002-9939(1972)0295070-0
Keywords: Schauder basis, representation of measurable functions, convergence in measure, asymptotic convergence
Article copyright: © Copyright 1972 American Mathematical Society