an infinite-dimensional and discontinuous setting. Fourthly, we impose additional topological assumptions on the underlying filtered space. This setting traces back to ideas employed by [@follmer72; @perkowski2015] in the context of the Föllmer measure. Thanks to an extension result for probability measures these conditions guarantee uniqueness and existence properties of the modified SMP, which lead to an explosion-type condition for martingality, c.f. Section \[Martingality on Standard Systems\].

Martingale criteria for non-negative local martingales driven by semimartingales are also interesting from an applications point of view. The class of semimartingales lies at the heart of financial modeling as it plays a fundamental role for stochastic integration, c.f. [@bichteler1981stochastic; @DellacherieMeyer78; @Pro] and [@DS], Chapter 7.3. In a semimartingale setting the seminal work [@DelbaenSchachermayer94; @Delbaen96thefundamental] relates absense of arbitrage to existence of an equivalent martingale measure (EMM). The existence of an EMM or more generally of changes of probability measures is deeply connected to the question when a candidate density process is a true martingale. Typically candidate processes are already non-negative local martingales. On a more practical side, changes of measures frequently lead to a substantial reduction of computational complexity. In mathematical finance for instance they arise as changes of numeraire and simplify the 