  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 others 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.
