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Garten and Knopp  introduced the notion of infinite iteration of Césaro (C1 ) averages, which they called H ∞ summability. Flehinger  (apparently unaware of ) produced the first nontrivial example of an H ∞ summable sequence: the sequence ﹛ai ﹜ ∞i=1 where at is 1 or 0 as the lead digit of the integer i is one or not. Duran  has provided an elegant treatment of H ∞ summability as a special case of summability with respect to an ergodic semigroup of transformations.
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