Two side shift on {0,1}^{\Z} is mixing of all order?

Question

I'm studying the ergodic theory. Is 2 side shift a mixing of all order?

How can I prove it?

Thank you for your help

Answer 1

Hint: If you are looking at a standard product measure, you may show this for cylinder sets (easy) and then use an approximation argument (if you are looking at measure theoretical mixing; for topological use that open sets contain cylinder sets).