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Pure strictly uniform models of non-ergodic measure automorphisms
- Publication Year :
- 2021
-
Abstract
- The classical theorem of Jewett and Krieger gives a strictly ergodic model for any ergodic measure preserving system. An extension of this result for non-ergodic systems was given many years ago by George Hansel. He constructed, for any measure preserving system, a strictly uniform model, i.e. a compact space which admits an upper semicontinuous decomposition into strictly ergodic models of the ergodic components of the measure. In this note we give a new proof of a stronger result by adding the condition of purity, which controls the set of ergodic measures that appear in the strictly uniform model.<br />Comment: 5 figures
- Subjects :
- Mathematics - Dynamical Systems
Primary 37B05, 37B20, Secondary 37A25
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2104.09604
- Document Type :
- Working Paper