The unique ergodicity of equicontinuous laminations (Q614286)

Let \(X\) be a locally compact metric space, \(X_0\) a relatively compact open subset of \(X\), \(\Gamma\) an equicontinuous and minimal pseudogroup of local homeomorphisms of \(X\) and \(\Gamma_0\) the restriction of \(\Gamma\) to \(X_0\). Under these assumptions, the author proves the existence of a nontrivial finite \(\Gamma_0\)-invariant Radon measure on \(X_0\) (Theorem 2.1). Moreover, if \(X\) is compact, then this measure is unique up to a scaling (Theorem 3.2).