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Quasi-disjointness, products and inverse limits

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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

  1. K. R. Berg, Quasi-disjointness in ergodic theory,Trans. Amer. Math. Soc., to appear.

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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

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