Open AccessPure strictly uniform models of non-ergodic measure automorphisms
Author(s) -
Tomasz Downarowicz,
Benjamin Weiss
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021140
Subject(s) - ergodic theory , measure (data warehouse) , stationary ergodic process , mathematics , pure mathematics , automorphism , invariant measure , extension (predicate logic) , set (abstract data type) , space (punctuation) , discrete mathematics , computer science , database , programming language , operating system
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.