Abstract
We prove that the set of expansive measures of a homeomorphism of a compact metric space is a [Formula: see text] subset of the space of Borel probability measures equipped with the weak* topology. Next that every expansive measure of a homeomorphism of a compact metric space can be weak* approximated by expansive measures with invariant support. In addition, if the expansive measures of a homeomorphism of a compact metric space are dense in the space of Borel probability measures, then there is an expansive measure whose support is both invariant and close to the whole space with respect to the Hausdorff metric. Henceforth, if the expansive measures are dense in the space of Borel probability measures, the set of heteroclinic points has no interior and the space has no isolated points.
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