The nonlinear filtering evolution can be interpreted as a dynamical system in the set of probability measures of the form η η n + 1 = Φ Φ n + 1 ( η η n ) where Φ Φ n + 1 stands for some mapping from the set of probability distribution into itself. For instance, the evolution of the one-step optimal predictor η η n ( d x n ) = p ( x n | y 0 , ⋯ ⋯ , y n − − 1 ) d x n