# Questions tagged [infinite-divisibility]

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### Can we show that the characteristic function of an infinitely divisible probability measure has no zeros

Let $E$ be a normed $\mathbb R$-vector space, $\mu$ be a probability measure on $\mathcal B(E)$ and $\varphi_\mu$ denote the characteristic function$^1$ of $\mu$. Assume $\mu$ is infinitely divisible, ...
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### Boudedness of linear operator between generalized Orlicz spaces

I am using the notations, definitions, and results of the Section X of  on generalized Orlicz spaces. We say that $\varphi : \mathbb{R} \rightarrow \mathbb{R}^+$ is a $\varphi$-function if it is ...
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### Uncountable divisible groups and the existence of order-preserving isomorphisms of their subsets

Let $(G,+,0,<)$ be an ordered divisible group of uncountable dimension. Consider the subset $G^{<0}$ of $G$. Question: Are $G$ and $G^{<0}$ isomorphic as ordered sets? Does there exist an ...
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### divisibility of uniform distribution [closed]

Let $X$ and $Y$ be independent and identically distributed random variables. Can $X+Y$ be a uniform distribution? (Please prove.) In other words, is a uniform distribution divisible? The meaning of "...
### Is $n=6$ the only integer satisfies ${\sigma}_x(n) \equiv 0\bmod{n}$ for every odd integer $x > 0$ and $2 (\bmod n)$ if $x$ is even integer? [closed]
After a few computations in wolfram alpha about the divisor function for some values of $n$ to look the behavior of $\sigma_x(n)\bmod n$ for $\,n=6,\,$ i got this result : $\sigma_x(6)=0 \bmod 6$ for \$...