(Easy to see this weighted mean is constant, and thus only possible limit. "better way?" is re: demonstrating convergence)
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Replying to @RadishHarmers
Variance{i copies of x_(k+i) for i=1,...,N} decreases as i increases unless it is 0, and thus has a limit.
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Replying to @ModelOfTheory @RadishHarmers
Let x_∞,...,x_(∞+N) be the limit of a convergent subsequence of adjacent (N+1)-tuples of elements of the sequence.
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Replying to @ModelOfTheory @RadishHarmers
Variance{i copies of x_(∞+i-1) for i=1,...,N} = Variance{i copies of x_(∞+i) for i=1,...,N}, but would be > if not 0.
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Replying to @ModelOfTheory @RadishHarmers
In "decreases as i increases", "i" should be "k".
6:57 PM - 16 Oct 2016
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