Further Properties of Sub-actions

Abstract

We enrich the discussion by taking into account less explored aspects of the set of continuous sub-actions, like the fact that, when considered up to constants, they form, in general, a non-compact subset of the quotient space. Such a property allows us to argue that, for Lipschitz continuous potentials that are not cohomologous to a constant, the separating sub-actions explicitly constructed in the previous chapter are quite particular and actually represent a small part of the whole set of Lipschitz continuous separating sub-actions.