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

By

SOMNATH DATTA, University of Georgia, Athens

and

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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