<t>yes. sorry. I meant the left hand side. I was thinking about the following counter-example:Take some omega such that U_i <= 0.5 if i \in V, and U_i > 0.5 if i \nin V, where V is the Vitali set. Also, fix f(x) = 0, if x <= 0.5 and f(x) = 1, if x > 0.5then, clearly f(U_i(w)) is not Lebesgue measura...