On Heyde’s Theorem for Probability Distributions on a Discrete Abelian Group
- 作者: Feldman G.1
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隶属关系:
- Verkin Institute for Low Temperature Physics and Engineering
- 期: 卷 97, 编号 1 (2018)
- 页面: 11-14
- 栏目: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225444
- DOI: https://doi.org/10.1134/S1064562418010027
- ID: 225444
如何引用文章
详细
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.
作者简介
G. Feldman
Verkin Institute for Low Temperature Physics and Engineering
编辑信件的主要联系方式.
Email: feldman@ilt.kharkov.ua
乌克兰, Kharkov, 61103