15. Continuation. The function 1/14 defined by (16), (18), and (19) is jointly measurable in u and t.

[The proof, which otherwise is essentially like that outlined in the preceding problem, requires the measurability in z and t of the integral g(z,t) = r- udF,(u) . -00 This integral is absolutely convergent for all t, since F, is a distribution belonging to an exponential family. For any z < 00, g(z, t) = lim gn(z, t), where 00 ( j ) [( j - 1 ) ( j )] gil ( z , r) = j~l Z - 2n F, z - ---r- - 0 - F, z - 2n - 0 , and the measurability of g follows from that of the functions gn' The inequalities corresponding to those obtained in step (2) of the preceding problem result from the property of the conditional one-sided tests established in Problem 22 of Chapter 3.]