The Lévy-Lindeberg central limit theorem in $L_{p}$, $0<p<1$
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- by Evarist Giné PDF
- Proc. Amer. Math. Soc. 88 (1983), 147-153 Request permission
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 $\mu$.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 147-153
- MSC: Primary 60B12; Secondary 60F05
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691297-1
- MathSciNet review: 691297