On random Fourier-stieltjes transforms

Let (Q, F, P) be a probability space, and let {uk}£ 1 be a se-quence of centered independent finite complex valued transition measures on Q x 8 (R"), ie,(i) for every we Q,{u:(w,)} is a sequence of finite complex valued measures on 8 (R");(ii) for every n# m and for every two Borel measurable simple functions p and b on R", the random vari-ables Jia p (u) un (w, du) and JRa b (u) um (w, du) are independent, and for every k> 1, Jad p (u) uk (w, du) is centered. Put Ve (w)=| uk (w, R") for the total variation norm and assume that {Ve} C Loo (P)