Types of convergence for sequences of probability densities and attractors

Some necessary and sufficient conditions on densities convergence for the existence of an ergoidc mixing, or exact dynamical system on a probability space given in [8] are extended to a measure space to obtain an ergodic, mixing or exact dynamical system on this measure space. More general sufficient conditions are given for the existence of those kinds of dynamical systems; as a consequence of these conditions it is obtained an ergodic, exact attractor for the orbits of almost every phase state. This orbits’ behaviour recall the thermodynamical evolution of systems from nonequilibrium to equilibrium states