Refer to Exercise 1 and examine the transformation T from the ergodicity viewpoint In Exercise 1 Let (, A, P) ( 0, 1), B(0,1),) where is the Lebesgue measure, and let the transformation T be defined by T(x) x 1 2, x ( 0, ), T(x) x , x( , 1) Then show that T is measurable and measure preserving ...

By Definition 8 T is ergodic if and only if every invarian ...

Refer to Exercise 1 and examine the transformation T from the ergodicity viewpoint. In Exercise 1 Let

Question:

Refer to Exercise 1 and examine the transformation T from the ergodicity viewpoint.
In Exercise 1
Let (Ω, A, P) = ([0, 1), B(0,1),λ) where λ is the Lebesgue measure, and let the transformation T be defined by
T(x) = x + 1/2, x ( [0, ½), T(x) = x = ½, x( [ ½, 1).
Then show that T is measurable and measure-preserving.