Conditional functions in the trajectory theory of dynamical systems

In this paper the notion of a conditional function of a trajectory partition of a dynamical system is introduced. The properties of conditional functions are to a large extent analogous to those of a Rohlin system of conditional measures, which permits us to apply conditional functions to the study of nonmeasurable partitions, for which systems of conditional measures do not exist. With the aid of conditional functions a simple condition for measurability of a discrete partition is given, and a system of invariants for simple partitions of type II is constructed – a system analogous to the Rohlin system of invariants of a measurable partition.
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