  The Bruss-Robertson inequality gives a bound on the maximal number of
elements of a random sample whose sum is less than a specified value, and the
extension of that inequality which is given here neither requires the
independence of the summands nor requires the equality of their marginal
distributions. A review is also given of the applications of the
Bruss-Robertson inequality, especially the applications to problems of
combinatorial optimization such as the sequential knapsack problem and the
sequential monotone subsequence selection problem.
