Abstract
Motivated by the notion of quasi-factor in topological dynamics, we introduce an analogous notion in the context of ergodic theory. For two processes,X andY , we haveX∡Y if and only ifY has a factor which is isomorphic to a quasi-factor ofX. On the other hand, weakly mixing processes can have nontrivial quasifactors which are not w.m. We characterize those ergodic processes which admit only trivial continuous ergodic quasi-factors, and use this characterization to conclude that a process with minimal selfjoinings is of this type. From this we derive the fact that for every suchX and any ergodicY eitherX ⊥Y orY extends some symmetric product ofX.
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References
R. Ellis and S. Glasner,Pure weak mixing, Trans. Am. Math. Soc.243 (1978), 135–146.
R. Ellis and S. Glasner,Iterated extensions, Ergodic Theory and Dynamical Systems, to appear.
R. Ellis, S. Glasner and L. Shapiro,PI-flows, Advances in Math.17 (1975), 213–260.
S. Glasner,Compressibility properties in topological dynamics, Am. J. Math.97 (1972), 148–171.
A. del Junco and D. Rudolph,Minimal selfjoinings and related properties, to appear.
M. Ratner,Joinings of horocycle flow, to appear.
D. Rudolph,An example of a measure-preserving map with minimal selfjoinings, and applications, J. Analyse Math.35 (1979), 97–122.
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Glasner, S. Quasi-factors in ergodic theory. Israel J. Math. 45, 198–208 (1983). https://doi.org/10.1007/BF02774016
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DOI: https://doi.org/10.1007/BF02774016