Let {Xn, n >0} be a sequence of independent identically distributed (iid) continuous random variables. Then, the sequences of upper record times, T^U_n , and upper records, X^U_n , are defined as: T^U_1 = 1 with probability one, X^U_1= X_1 and for n > 1, T^U_n = min{ j : j > T^U_{n−1}, X_j > X_{T^U_n−1:T^U_{n−1}}, where X_{i:m} stands for the ith order statistic from a random sample of size m. In this paper, we develop the random variable xn(a) by definition a random variable xn(A), the number of observations that fall into a random region determined by a Borel set A that is subsets of positive real number and the nth upper record. We investigated the asymptotic behavior of xn(A) in a sequence of iid and absolutely continuous random variables.

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