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Timeline for Do these limits exist?

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Jun 28, 2018 at 14:31 comment added user44191 $\alpha = \frac{\sqrt{2}}{2}(x_0+x_1)$; then $\beta$ is $\frac{1}{2}(x_{-1}+2x_0+x_1)$, and $\beta^n$ is a centered binomial distribution, so the limit is $1$.
Jun 28, 2018 at 13:47 comment added MSMalekan @user44191 What do you mean by properly scaled indicator function on 0,1∈Z?
Jun 28, 2018 at 3:48 comment added user44191 I think it is sometimes $1$; consider $\alpha$ the properly scaled indicator function on $0, 1 \in \mathbb{Z}$?
Jun 28, 2018 at 1:34 comment added MSMalekan @usser44191: No, I think these limits are always equal zero.
Jun 27, 2018 at 21:37 comment added user44191 Do you have any examples where the limit is neither $0$ nor $1$?
Jun 27, 2018 at 17:57 history edited MSMalekan CC BY-SA 4.0
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Jun 27, 2018 at 17:44 history edited Joe Silverman CC BY-SA 4.0
Improved formatting
Jun 27, 2018 at 17:18 history asked MSMalekan CC BY-SA 4.0