Abstract: We study the almost sure convergence of weighted sums of dependent random variables to a positive and finite constant, in the case when the random variables have either mean zero or no mean at all. These are not typical strong laws and they are called exact strong laws of large numbers. We do not assume any particular type of dependence and furthermore consider sequences which are not necessarily identically distributed. The obtained results may be applied to sequences of negatively associated random variables.

2010 AMS Mathematics Subject Classification: Primary: 60F15; Secondary: 60F05.

Keywords and phrases: Strong law of large numbers, almost sure convergence, slowly varying functions, negative association.