Independent Linear Statistics on Finite Abelian Groups
We give a complete description of the class of all finite Abelian groups X for which the independence of linear statistics L 1 = α1(ξ1) + α2(ξ2) + α3(ξ3) and L 2 = β1(ξ1) + β2(ξ2) + β3(ξ3) (here, ξ j , j = 1, 2, 3, are independent random variables with values in X and distributions μ j ; α j and β...
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| Date: | 2001 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4266 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510398505025536 |
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| author | Graczyk, P. Fel'dman, G. M. Грачик, П. Фельдман, Г. М. Грачик, П. Фельдман, Г. М. |
| author_facet | Graczyk, P. Fel'dman, G. M. Грачик, П. Фельдман, Г. М. Грачик, П. Фельдман, Г. М. |
| author_sort | Graczyk, P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:45Z |
| description | We give a complete description of the class of all finite Abelian groups X for which the independence of linear statistics L 1 = α1(ξ1) + α2(ξ2) + α3(ξ3) and L 2 = β1(ξ1) + β2(ξ2) + β3(ξ3) (here, ξ j , j = 1, 2, 3, are independent random variables with values in X and distributions μ j ; α j and β j are automorphisms of X) implies that either one, or two, or three of the distributions μ j are idempotents. |
| first_indexed | 2026-03-24T02:56:22Z |
| format | Article |
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| id | umjimathkievua-article-4266 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:56:22Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/18/76f7c4cf061b825995f7500d7c691a18.pdf |
| spelling | umjimathkievua-article-42662020-03-18T20:25:45Z Independent Linear Statistics on Finite Abelian Groups Независимые линейные статистики на конечных абелевых группах Graczyk, P. Fel'dman, G. M. Грачик, П. Фельдман, Г. М. Грачик, П. Фельдман, Г. М. We give a complete description of the class of all finite Abelian groups X for which the independence of linear statistics L 1 = α1(ξ1) + α2(ξ2) + α3(ξ3) and L 2 = β1(ξ1) + β2(ξ2) + β3(ξ3) (here, ξ j , j = 1, 2, 3, are independent random variables with values in X and distributions μ j ; α j and β j are automorphisms of X) implies that either one, or two, or three of the distributions μ j are idempotents. Наведено повний опис класу всіх скінченних абелевих груп $X$, для яких з незалежиосты лінійних статистик $L1 = α_1(ξ_1) + α_2(ξ_2) + α_3(ξ_3)$ та $L_2 = β_1(ξ_1) + β_2(ξ_2) + β_3(ξ_3)$ ($ξ_j, j = 1, 2, 3,$ — незалежны випадковы величини зi значеннями в $X$ i з розподілами $μ_j, α_j, β_j$ — автоморфізми групи $X$) випливає, що або один, або два, або три з розподилів $μ_j$ є ідемпотентами. Institute of Mathematics, NAS of Ukraine 2001-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4266 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 4 (2001); 441-448 Український математичний журнал; Том 53 № 4 (2001); 441-448 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4266/5236 https://umj.imath.kiev.ua/index.php/umj/article/view/4266/5237 Copyright (c) 2001 Graczyk P.; Fel'dman G. M. |
| spellingShingle | Graczyk, P. Fel'dman, G. M. Грачик, П. Фельдман, Г. М. Грачик, П. Фельдман, Г. М. Independent Linear Statistics on Finite Abelian Groups |
| title | Independent Linear Statistics on Finite Abelian Groups |
| title_alt | Независимые линейные статистики на конечных абелевых
группах |
| title_full | Independent Linear Statistics on Finite Abelian Groups |
| title_fullStr | Independent Linear Statistics on Finite Abelian Groups |
| title_full_unstemmed | Independent Linear Statistics on Finite Abelian Groups |
| title_short | Independent Linear Statistics on Finite Abelian Groups |
| title_sort | independent linear statistics on finite abelian groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4266 |
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