The concepts of periodicity and aperiodicity are extended so as to apply to any measurable non-singular transformation T in s-finite measure space (X,v,M). Aperiodicity of T may then be characterized by the existence of sweep-out sets with certain properties and turns out to be closely related to the existence of a strong generator for the s-algebra v. This extends recent results of Parry and Rokhlin obtained for Lebesgue spaces.
|Number of pages||11|
|Journal||Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete|
|Publication status||Published - 1969|