Sankhya: The Indian Journal of Statistics
1997, Volume 59, Series A, Pt. 2, 167-174
A UNIFORM L1 LAW OF LARGE NUMBERS FOR FUNCTIONS ON A TOTALLY BOUNDED METRIC SPACE
SOMNATH DATTA, University of Georgia, Athens
JAMES F. HANNAN, Michigan State University, East Lansing
SUMMARY. Let S be a totally bounded metric space and B(S) the space of bounded real function on S. We obtain a L1 law of large numbers in the uniform (sup) norm for averages associated with arrays in B(S).
AMS (1991) subject classification. Primary 62F25, secondary 62F12.
Key words and phrases. Laws of large numbers, L1 convergence, uniform convergence .
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