Let (, A) = ([0, 1), B(0,1)), and let the transformation T be defined by T(x) =
Question:
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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For every 0 x 1 clearly T 1 c 2 x cx cx x and if a probability measure P is mea...View the full answer
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Related Book For 
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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