Sankhya: The Indian Journal of Statistics1997, Volume 59, Series A, Pt. 3, 301-310
LAWS OF LARGE NUMBERS FOR UNCORRELATED CESARO UNIFORMLY INTEGRABLE RANDOM VARIABLES
DIETER LANDERS, University of Cologne
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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