An Endomorphism Whose Square Is Bernoulli
نویسندگان
چکیده
One of the corollaries of Ornstein’s isomorphism theorem is that if (Y, S, ν) is an invertible measure preserving transformation and (Y, S, ν) is isomorphic to a Bernoulli shift then (Y, S, ν) is isomorphic to a Bernoulli shift. In this paper we show that noninvertible transformations do not share this property. We do this by exhibiting a uniformly 2-1 endomorphism (X, σ, μ) which is not isomorphic to the one sided Bernoulli 2 shift. However (X, T , μ) is isomorphic to the one sided Bernoulli 4 shift.
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