Sheaves of Measures and KMS-Weights on Topological Graph Algebras

Abstract

We show that the collection of regular Borel measures on a second-countable locally compact Hausdorff space has the structure of a sheaf. With this we give an alternate description of the pullback of a regular Borel measure along a local homeomorphism. We are able to use these tools to give a description of the KMS-weights for the gauge-action on the graph C*-algebra of a second-countable topological graph in terms of sub-invariant measures on the vertex space of said topological graph.