=+13.17. Let S = {0,1), and define a map T from sequence space S" to [0,1] by Tw -Ex _, a.(@)/2". Define a map U of [0, 1] to S" by Ux = (df( x), d2(x) ,... ), where the da(x) are the digits of the nonterminating dyadic expansion of x

(and d (0) = 0). Show that T is measurable 6/9 and that U is measurable 9/ 6. Let P be the measure specified by (2.21) for Po =p1 = 3. Describe PT- and AU -!.