  We prove a result on equilibrium measures for potentials with summable
variation on arbitrary subshifts over a countable amenable group. For finite
configurations $v$ and $w$, if $v$ is always replaceable by $w$, we obtain a
bound on the measure of $v$ depending on the measure of $w$ and a cocycle
induced by the potential.
  We then use this result to show that under this replaceability condition, we
can obtain bounds on the Lebesgue-Radon-Nikodym derivative $d (\mu_\phi \circ
\xi ) / d\mu $ for certain holonomies $\xi$ that generate the homoclinic
(Gibbs) relation.
  As corollaries, we obtain extensions of results by Meyerovitch and
Garcia-Ramos and Pavlov to the countable amenable group subshift setting. Our
methods rely on the exact tiling result for countable amenable groups by
Downarowicz, Huczek, and Zhang and an adapted proof technique from Garcia-Ramos
and Pavlov.
