Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 2, 167-174

A UNIFORM * L _{1}* 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 *L _{1}* law of large numbers in the uniform (sup) norm for averages associated with arrays in B

*AMS (1991) subject classification.* Primary 62F25, secondary 62F12.

*Key words and phrases*. Laws of large numbers, *L _{1}* convergence, uniform convergence .