Alsmeyer, Gerold - In: Statistics & Probability Letters 12 (1991) 4, pp. 285-287
Let Ik(n) denote the kth largest intervals generated by 0, X1,..., Xn-1, 1 where X1, X2, ... are i. This note provides a complete answer to the question for which class of sequences k(n) the interval Ik(n)(n) is hit only finitely o as well as infinitely often (a.s.).