On Heyde’s Theorem for Probability Distributions on a Discrete Abelian Group
- Авторы: Feldman G.1
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Учреждения:
- Verkin Institute for Low Temperature Physics and Engineering
- Выпуск: Том 97, № 1 (2018)
- Страницы: 11-14
- Раздел: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225444
- DOI: https://doi.org/10.1134/S1064562418010027
- ID: 225444
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Аннотация
Let X be a countable discrete Abelian group containing no elements of order 2. Let α be an automorphism of X. Let ξ1 and ξ2 be independent random variables with values in the group X and distributions μ1 and μ2. The main result of the article is the following statement. The symmetry of the conditional distribution of the linear form L2 = ξ1 + αξ2 given L1 = ξ1 + ξ2 implies that μj are shifts of the Haar distribution of a finite subgroup of X if and only if α satisfies the condition Ker(I + α)= {0}. Some generalisations of this theorem are also proved.
Об авторах
G. Feldman
Verkin Institute for Low Temperature Physics and Engineering
Автор, ответственный за переписку.
Email: feldman@ilt.kharkov.ua
Украина, Kharkov, 61103