Summary
We work within the class of ergodic measure-preserving transformations on probability spaces (called processes). Quasi-disjointness between two such objects has been defined in terms of the properties of the pieces of a certain decomposition of the product space. A large class
of processes is known to be quasi-disjoint from every ergodic process. In this paper we establish that
is closed under certain natural constructions. If two objects in
have an ergodic product, then that product is in
. The inverse limit of objects in
is in
, provided the index set is countable and directed.
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References
K. R. Berg, Quasi-disjointness in ergodic theory,Trans. Amer. Math. Soc., to appear.
H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation,Math. Systems Theory 1 (1967), 1–49.
W. Parry,Math. Reviews 35 (1968), #4369.
V. S. Varadarajan, Groups of automorphisms of Borel spaces,Trans. Amer. Math. Soc. 109 (1963), 191–220.
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This research was supported in part by National Science Foundation Grant GP 9605.
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Berg, K.R. Quasi-disjointness, products and inverse limits. Math. Systems Theory 6, 123–128 (1972). https://doi.org/10.1007/BF01706083
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DOI: https://doi.org/10.1007/BF01706083