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Results tagged with equidistribution
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user 169474
2
votes
Accepted
Equidistribution and moments
Yet, It true, because the uniform distribution on $[0,1]$ is characterized by its moments. When a probability measure $\mu$ is characterized by its moments and $(\mu_n)$ is any sequence of probability …
- 3,808
2
votes
Accepted
Is equal natural density on intervals with matching areas but opposite signs sufficient to u...
Let us take the $\theta_n$ in the interval $[0,2\pi)$.
For every $N \ge 1$, set
$$\mu_N = \frac1N\sum_{n=1}^N\delta_{\theta_n} \text{ and } \nu_N := \mathbb{1}_{(0,\pi)\cup(\pi,2\pi)}\mu_N.$$
The exis …
- 3,808