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Let be a sequence of independent identically distributed observations with a common mean . Assume that with probability 1. We show that for each there exists an integer , a finite-valued statistic and a real-valued function defined on such that ) ; ii) . Thus we have a recursive-like estimate of , for which the data are summarized for each by one of states and which converges to within of with probability 1. The constraint on memory here is time varying as contrasted to the time-invariant constraint that would have for all .