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Research Area: Ergodic Theory.

My Advisor: William,A,Veech

About the Problem I am doing:

1.

Once given a partition P, then we can get the shift transformation T_s on the infinite product space H of the alphabet set (according to the atoms in P) corresponding to T.The ivariant measure on H is naturally induced by the measure on X,the original space. And once T is measurable(m.p.),T_s is measurable (m.p.).Conversely results were gain during the process of the study of the isomorphism of the Bernoulli Process. But we know the shift transformation depends on the measure defined crucially(ex., Bernoulli shift which has entropy ...,Natural Code of interval exchange, which has entropy 0).So the question is once we have a typical language, we define the measure based on the frequency of the cylinder, how can we say it is a m.p.t.?

2. Primality of Three-interval Exchange Transformations