Random Sieves and Generalized Leader-election Procedures

A random sieve of the set positive integers N is an infinite sequence nested subsets = S0 ⊃ S1 S2 · such that Sk obtained from Sk−1 by removing elements with indices outside Rk and enumerating remaining inthe increasing order. Here R1 , R2 . a independent copies R ⊂ N. We prove general limit theorems for Sn related functionals, as n → ∞.