FF-expansivity for Borel measures

We introduce the notion of FF-expansive measure by making the dynamical ball in [4] to depend on a given subset FF of the set of all the reparametrizations HH. We prove that these measures satisfy some interesting properties resembling the expansive ones. These include the equivalence with expansivity when F=HF=H, the vanishing along the orbits, the absence of singularities in the support, the FF-expansivity with respect to time t  -maps, the invariance under equivalence and the characterization for suspensions. We also analyze the support of the FF-expansive measures and prove that there exists a dense subset of measures (in the set of FF-expansive measures) all of them with a common support. Finally, we extend to flows the recent result for homeomorphisms in [11].