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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Lévy-Lindeberg central limit theorem in Orlicz spaces $L_{\Phi }$
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by Anna T. Ławniczak PDF
Proc. Amer. Math. Soc. 89 (1983), 673-679 Request permission


An ${L_\phi }(T,\mathcal {F},m)$-valued random element $X$, where $\Phi ({t^{1/2}})$ is equivalent to a concave function, satisfies the Lévy-Lindeberg central limit theorem if and only if it is centered and pre-Gaussian; that is, if and only if $EX(t) = 0$ $m$-a.e. and ${\{ E{X^2}(t)\} ^{1/2}} \in {L_\phi }$.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 673-679
  • MSC: Primary 60B12; Secondary 60F05, 60G17
  • DOI:
  • MathSciNet review: 718995