Abstract
A notion of “nesting” for very weakly Bernoulli distributions is developed and used to prove that any two-point extension of a Bernoulli shift, if it has ergodic square, must itself be Bernoulli.
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This work was supported in part by N.S.F. Grant NCS76-09159.
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Rudolph, D.J. If a two-point extension of a Bernoulli shift has an ergodic square, then it is Bernoulli. Israel J. Math. 30, 159–180 (1978). https://doi.org/10.1007/BF02760837
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DOI: https://doi.org/10.1007/BF02760837