Janet Whalen Kammeyer

A complete classification of the two-point extensions of a multidimensional bernoulli shift

A theorem is proven which gives five characterizations of a multidimensional Bernoulli shift. The two-point extensions of a multidimensional Bernoulli shift are classified completely. If such an extension is weakly mixing then it must be Bernoulli; otherwise, it is isomorphic to one of 2n specific trivial extensions. This result is extended to multidimensional Bernoulli flows and Bernoulli shifts of infinite entropy.

The isomorphism theorem for relatively finitely determined Z n -actions

Any two ergodic Zn-actions which are finitely determined relative to a common factor are isomorphic if and only if they have the same entropy.