In [9] we introduced a new framework for asymptotic probabilities. in which a r i-add~t~ve measure is defined on the sample space of all sequences A =< dl.d?. . d, > of finite models. where the uniberse of sf,, is { I . 2. ...n ) . In this framework we Investigated the strong 0-1 law for sentences. whlch states that each sentence either holds in d,, eventually almost surely or fails In d,, even...

in a celebrated work by shao [13] several inequalities for negatively associated random variables were proved. in this paper we obtain some maximal inequalities for associated random variables. also we establish a maximal inequality for demimartingales which generalizes and improves the result of christofides [4].