Tagging - 2022-09-25

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new-tag A new tag uniform-distribution-modulo-1. A tag-excerpt was created, too.

new-tag A new tag uniform-distribution-modulo-1. A tag-excerpt was created, too. There already is a tag called equidistribution.

Q: If $(x_n)$ is ud mod $1$ and $(y_n)$ satisfies $\lim_{N\to \infty} \frac 1N \sum_{n=1}^N |y_n|=0$ then $(x_n+y_n)$ is ud mod $1$

If $(x_n)$ is ud mod $1$ and $(y_n)$ satisfies $$\lim_{N\to \infty} \frac 1N \sum_{n=1}^N |y_n|=0$$ then $(x_n+y_n)$ is ud mod $1$. Since this comes as an exercise after the first two sections of the first chapter of Uniform Distribution of Sequences, I guess we need to use the Weyl criterion. ...