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Given a stream with frequencies f d , for d ∈ [n], we characterize the space necessary for approximating the frequency negative moments F p = |f d | p , where p < 0 and the sum is taken over all items d ∈ [n] with nonzero frequency, in terms of n, , and m = |f d |. To accomplish this, we actually prove a much more general result. Given any nonnegative and nonincreasing function g, we characterize the space necessary for any streaming algorithm that outputs a (1± )-approximation to g(|f d |),doi:10.3929/ethz-b-000112083 fatcat:xmwgi3vgafhzheenstdp37tor4