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It is possible to further strengthen the theorem and to specify the sizes of the sets along which such a convergence takes place.
Let i be a reference point of the given sequence of length n, d = g g … g i … g n−1 g n A generalized sequence of length 2, g ig k is constructed if k satisfies k ∈ [ i− w b i+ w f ], k ≠ i, 1 ≤ i ≤ n−1, where w b and w f specify the sizes of backward- and forward- windows (0 ≤ w b ≤ i−1, 1≤ w f ≤ n− i), respectively.
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