A Simple Derivation of a Complicated Prophet Region

A straightforward proof of a result of R. P. Kertz (1986, J. Multivariate Anal.19, 88–112) is given, concerning the complete comparison of the values to a statistician, observing sequentially a sequence X1, …, Xn of iid, [0, 1]-valued random variables, and the value to a prophet, observing that same sequence, and picking the largest observation to occur.