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.