Question: Let (, A) = ([0, 1), B(0,1)), and let the transformation T be defined by T(x) = cx, x ( [0, 1), where c is

Let (Ω, A) = ([0, 1), B(0,1)), and let the transformation T be defined by
T(x) = cx, x ( [0, 1), where c is a constant in (0, 1).
Then show that there is no probability measure P on B(0,1) such that P({x}) = 0, x ( [0, 1), and for which the transformation T is measure-preserving.

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