Markov type properties for mixtures of probability measures (Q1093267)

We show that, given a general Markov type property M, and a finite- dimensional set of probability measures \({\mathcal H}\), the set of elements of \({\mathcal H}\) having M can be described by finitely many quadratic equations. We apply the result to the problem of the global Markov property for nonextremal Gibbs states.