Complete Convergence for M-Pairwise Negatively Dependent Random Variables

Hsu and Robbins (1947) introduce the concept complete convergence as follows. A sequence of random variables is said to converge completely a constant if for all The converse true are independent. They also show that arithmetic means independent identically distributed converges expected value variance summands finite. Erdös proved converse. result Hsu-Robbins-Erdös fundamental theorem in probability theory has been generalized extended several directions by many authors. In this paper, let be positive constants with m-pairwise negatively dependent variables. We study under mild condition . Our results obtained paper generalize corresponding ones pairwise