with its borelian subset and P the Lebesgue measure over [0,1].

Let , k from 1 to 2^(n-1).

I have showed that the family is mutually independent.

Now,

Let from [0,1] in {0,1} (k from 1 to 2^(n-1))

I have to show that the random variables are mutually independent too, but I can't get there...

Thank you for helping me