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The Lévy-Lindeberg central limit theorem in $ L\sb{p}$, $ 0<p<1$

Author: Evarist Giné
Journal: Proc. Amer. Math. Soc. 88 (1983), 147-153
MSC: Primary 60B12; Secondary 60F05
MathSciNet review: 691297
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Abstract: A $ {L_p}(T,\Sigma ,\mu )$-valued r.v. $ X$, $ 0 < p < 1$, satisfies the Lévy-Lindeberg central limit theorem if and only if it is centered and pregaussian, that is, if and only if $ \int\limits_T {{{(E{X^2}(t))}^{p/2}}d\mu (t) < \infty } $ $ EX(t) = 0$-a.e. and $ \mu $.

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Article copyright: © Copyright 1983 American Mathematical Society