Pure strictly uniform models of non-ergodic measure automorphisms

2021/04/19 by Downarowicz, Tomasz, Weiss, Benjamin
#37B20 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37B05 #Secondary 37A25

paper · doi:10.48550/arxiv.2104.09604

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.

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