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- W4300092011 abstract "It is well known Heyde's characterization of the Gaussian distribution on the real line: Let $xi_1, xi_2,dots, xi_n$, $nge 2,$ be independent random variables, let $alpha_j, beta_j$ be nonzero constants such that $beta_ialpha_i^{-1} + beta_jalpha_j^{-1} ne 0$ for all $i ne j$. If the conditional distribution of the linear form $L_2 = beta_1xi_1 + beta_2xi_2+ cdots + beta_nxi_n$ given $L_1 = alpha_1xi_1 + alpha_2xi_2+cdots + alpha_nxi_n$ is symmetric, then all random variables $xi_j$ are Gaussian. We prove an analogue of this theorem for two independent random variables in the case when they take values in the group of $p$-adic numbers $Omega_p$, and coefficients of linear forms are topological automorphisms of $Omega_p$." @default.
- W4300092011 created "2022-10-03" @default.
- W4300092011 creator A5020668017 @default.
- W4300092011 date "2014-03-05" @default.
- W4300092011 modified "2023-10-18" @default.
- W4300092011 title "On a characterization theorem for the group of p-adic numbers" @default.
- W4300092011 doi "https://doi.org/10.48550/arxiv.1403.1106" @default.
- W4300092011 hasPublicationYear "2014" @default.
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