Density topologies and the marginal strong lifting problem for hyperstonian spaces

We investigate properties of density topologies and of topological measure spaces whose topologies are density topologies, motivated by the search for necessary as well as sufficient conditions for the canonical strong lifting of a hyperstonian space to be a marginal. For topological probability spaces we establish relations between the existence of strong liftings and the marginal property of the canonical strong lifting of their hyperstonian space, building on earlier work.