Thin times and random times’ decomposition

The paper defines and studies thin times which are random whose graph is contained in a countable union of graphs stopping with respect to reference filtration F. We show that generic time can be decomposed into thick parts, where the second avoiding all F-stopping times. Then, for given ?, we introduce F?, smallest right-continuous containing F making ? time, that, each F-martingale an F?-semimartingale, i.e., hypothesis (H?) (F,F?) holds. present applications honest times, seen as last passage showing classes filtrations only support or accommodate well.