Let's not be so technical. Choose a number x in [0,1] whose decimal representation is .x_1x_2x_3x_4... . Then the random variables y=x_1x_3x_5... and z=x_2x_4x_6... are independent and uniformly distributed.
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- Title: What are two independent, uniformly distributed random variables on the unit interval? - MathOverflow
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