Asymptotic behavior of continuous set-indexed martingales

in this paper. Following the Knight's approach. we solve a convergence prob lem Tot set-indexed martingales. For this purpose, we first define a tightn ess criterion For set-indexed continuous processes. The core oi this: chara cterization is connected with a weaker definition of continuity and hence t he use of the corresponding topology, and with the Fact that indices take v alues in a semilattice of closed subsets. Then. we give an effective lightn ess criterion by means of an estimate For a majorizing measure defined on t he space. We finally prove under this set-indexed framework a theorem simil ar to the Knight's.