Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 180-190 |
| Number of pages | 11 |
| Journal | Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete |
| Volume | 13 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1969 |