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 2 ⁿ specific trivial extensions. This result is extended to multidimensional Bernoulli flows and Bernoulli shifts of infinite entropy. This work supported in part by N.S.F. Grant DMS-85-04701 and by the University of Maryland Department of Mathematics.