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,

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.