  Following works of Furstenberg and Nevo and Zimmer we present an outline of a
theory of stationary (or m-stationary) dynamical systems for a general acting
group G equipped with a probability measure m. Our purpose is two-fold: First
to suggest a more abstract line of development, including a simple structure
theory. Second, to point out some interesting applications; one of these is a
Szemeredi type theorem for SL(2,R).
