Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 3, 301-310

LAWS OF LARGE NUMBERS FOR UNCORRELATED CESARO UNIFORMLY INTEGRABLE RANDOM VARIABLES

By

DIETER LANDERS, University of Cologne

And

LOTHAR ROGGE, University of Duisburg, Germany

SUMMARY. It is proved for non-negative uncorrelated random variables that Cesaro-uniform integrability implies the weak law of large numbers and strong Cesaro-uniform integrability implies the strong law of large numbers. A counter-example shows that the non-negativity assumption is essential in this context.

 AMS (1991) subject classification. 60F25, 60F15, 60F05.

Key words and phrases. Weak law of large numbers, strong law of large numbers, uncorrelated large numbers, uncorrelated random variables, uniform intregrability, Cesaro uniform intregrability.

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