Postprint version. Published in Stochastic Analysis and Applications, Volume 5, Issue 3, January 1, 1987, pages 299-310.
Copyright © 1987 Taylor & Francis. This is an electronic version of an article published in Stochastic Analysis and Applications.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1080/07362998708809118.
Applications of the original prophet inequalities of Krengel and Sucheston are made to problems of order selection, non-measurable stop rules, look-ahead stop rules, and iterated maps of random variables. Also, proofs are given of two results of Hill and Hordijk concerning optimal orderings of uniform and exponential distributions