The Lévy-Lindeberg central limit theorem in Orlicz spaces 𝐿_{Φ}

Ławniczak, Anna T.

doi:10.1090/S0002-9939-1983-0718995-5

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

Abstract:

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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