If the (T; Id) automorphism is Bernoulli then the (T; Id) endomorphism is standard
For any 1-1 measure preserving map T of a probability space we can form the (T; Id) and (T;T 1 ) automorphisms as well as the corresponding endomorphisms and decreasing sequence of -algebras. In this paper we show that if T has zero entropy and the (T; Id) automorphism is isomorphic to a Bernoulli shift then the decreasing sequence of -algebras generated by the (T; Id) endomorphism is standard. We also show that if T has zero entropy and the (T 2 ; Id) automorphism is isomorphic to a Bernoulli shift then the decreasing sequence of -algebras generated by the (T;T 1 ) endomorphism is standard.