  We characterize the event of convergence of a local supermartingale.
Conditions are given in terms of its predictable characteristics and quadratic
variation. The notion of extended local integrability plays a key role. We then
apply these characterizations to provide a novel proof for the sufficiency and
necessity of Novikov-Kazamaki type conditions for the martingale property of
nonnegative local martingales with jumps.
