Kingman's subadditive ergodic theorem
The Bruss-Robertson Inequality:Elaborations, Extensions, and Applications
The Bruss-Robertson inequality gives a bound on themaximal number of elements of a random sample whose sum is less than a specifiedvalue, and the extension of that inequality which is given hereneither 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 subsequences in the sequence of fractional parts of multiples of an irrational.
Catching small sets under Flows
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