On the Expansiveness of Invariant Measures under Pseudogroups

In this paper, we define and study weak expansive and expansive measures for pseudogroups, these two notions appear when analyzing the role of the generating set. We investigate the relations between such properties. We also provide a criterion for a measure to be weak expansive through the positivity of its entropy, generalizing the work of Arbieto and Morales. We also show that in some settings equicontinuous pseudogroups have no expansive measures.