Sankhya: The Indian Journal of Statistics

1989, Volume 51, Series A, Pt. 3, pp. 309--317

UNIFORM INTEGRABILITY IN THE CESÀRO SENSE AND THE WEAK LAW OF LARGE NUMBERS

By

TAPAS K. CHANDRA, Indian Statistical Institute

SUMMARY. It is shown here that L1 convergence holds in large number of cases where the WLLN holds; in fact, it is shown that the proof of the stronger fact is somewhat easier and more straightforward. In particular, several extensions and variations of the classical Khinchin WLLN are obtained.

AMS (1985) subject classification. Primary 60F05; secondary 60G42.

Key words and phrases. Uniform integrability, uniform integrability in the Cesaro sense, weak law of large numbers, martingale-difference sequence, $/phi$-mixing sequence.

This article in mathematical reviews.