The generic extension of a Bernoulli shift is relatively mixing
摘要: Well known theorems of Halmos and Rokhlin state that the generic transformation is weakly mixing and not mixing.Recently M. Schnurr proved that if one considers the set of transformations which leave invariant a subalgebra of the Borel algebra of [0, 1] generically these transformations will be weakly mixing relatively to this subalgebra. This was improved by Glasner and Weiss to the fact that, when one fixes the action on the subalgebra, it remains true that the generic extension is relatively weakly mixing. These can be considered as a relativized version of the Halmos Rokhlin theorem. However the relativized version of the meager property of mixing is not true for Bernoulli shifts. The purpose of the lecture will be to prove this fact.