## A Non-Bernoulli Skew Product |

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A C X assume Bernoulli shift bijections CLASS OF LOOSELY completely positive entropy concerned with properties CONSTRUCTING AN EXAMPLE defined degree of Doctor distance less distributed processes Doctor of Philosophy entropy of S,P ergodic dynamical system Ergodic Theory f matches Feldman fully adequate g*-evenly distributed h metric indices differ infinite past initial substring integer irrational rotation isomorphic Israel Journal iterated logarithm Journal of Math K-automorphisms l)-blocks l)-subblocks large numbers law of large least Lebesgue measure length greater Let S,P Let S,P,X loosely Bernoulli processes measure space measure zero Melijson METRICS ON STRINGS n-box N-l N-l N-strings names of x,y Note overlap P-name partition past atoms pre-Bernoulli processes process S,P processes are loosely Proof Proposition 4.3 Proposition 5.2 random variables rank one process read this thesis Rochlin towers S~nP say a process scope and quality STRINGS OF SYMBOLS subblocks Theorem zero entropy