The almost Borel structure of surface diffeomorphisms, Markov shifts and their factors
The almost Borel structure of surface diffeomorphisms, Markov shifts and their factors
Extending work of Hochman, we study the almost-Borel structure, i.e., the nonatomic invariant probability measures, of symbolic systems and surface diffeomorphisms. We first classify Markov shifts and characterize them as strictly universal with respect to a natural family of classes of Borel systems. We then study their continuous factors showing …