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Proceedings of the American Mathematical Society

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

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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