For a long time deterministicand statisticaldescriptionsof physical phenomena existed in distinctmathematical environments. Topology, flmctionalanalysis,and differentialgeometry played the main rolein deterministicmechanics, whereas measure theory and the theory of stochasticprocesses were the tools of statisticalmechanics. Furthermore, statisticaldescriptionswere usually associated with the lack of information on the precisedynamical specificationof systems with a large number of degrees of freedom.