The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which beta there are gauge invariant beta-KMS weights on a simple graph C*-algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.
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