The real interval [0,1) with Lebesgue measure is commonly used as a probability space; in this case, the measure of cases where one rolls a 6 has Lebesgue measure 1/6, we can without loss of generality say it's the interval [0,1/6), and we can linearly pair every point in this set with a point in the set [1/6,1) to get a nice measurable correspondence. It's just that this fails to preserve measure.

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