On the Skitovich-Darmois Theorem on Abelian Groups
We prove theorems that generalize the Skitovich-Darmois theorem to the case where independent random variables ξj, j = 1, 2, ..., n, n ≥ 2, take values in a locally compact Abelian group and the coefficients αj and βj of the linear forms L 1 = α1ξ1 + ... + αnξn and L 2 = β1ξ1 + ... + βnξn are automo...
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| Дата: | 2004 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2004
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3847 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509979958575104 |
|---|---|
| author | Myronyuk, M. V. Миронюк, М. В. |
| author_facet | Myronyuk, M. V. Миронюк, М. В. |
| author_sort | Myronyuk, M. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:12:30Z |
| description | We prove theorems that generalize the Skitovich-Darmois theorem to the case where independent random variables ξj, j = 1, 2, ..., n, n ≥ 2, take values in a locally compact Abelian group and the coefficients αj and βj of the linear forms L 1 = α1ξ1 + ... + αnξn and L 2 = β1ξ1 + ... + βnξn are automorphisms of this group. |
| first_indexed | 2026-03-24T02:49:43Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3847 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:49:43Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/8e/7f5be542a1c12172ca21f5831637288e.pdf |
| spelling | umjimathkievua-article-38472020-03-18T20:12:30Z On the Skitovich-Darmois Theorem on Abelian Groups До теореми Скитовича- Дармуа па абелевих групах Myronyuk, M. V. Миронюк, М. В. We prove theorems that generalize the Skitovich-Darmois theorem to the case where independent random variables ξj, j = 1, 2, ..., n, n ≥ 2, take values in a locally compact Abelian group and the coefficients αj and βj of the linear forms L 1 = α1ξ1 + ... + αnξn and L 2 = β1ξ1 + ... + βnξn are automorphisms of this group. Доведено теореми, що узагальнюють теорему Скитовича - Дармуа на випадок, коли незалежні випадкові величини $ξ_j,\; j = 1, 2, ..., n, n ≥ 2$, набувають значень у локально компактній абелевій групі, а коефіцієнти $α_j,\; β_j$- лінійних форм $L_1 = α_1ξ_1 + ... + α_nξ_n $ та $L_2 = β_1ξ_1 + ... + β_nξ_n$ є антоморфізмами групи. Institute of Mathematics, NAS of Ukraine 2004-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3847 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 10 (2004); 1342 – 1356 Український математичний журнал; Том 56 № 10 (2004); 1342 – 1356 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3847/4413 https://umj.imath.kiev.ua/index.php/umj/article/view/3847/4414 Copyright (c) 2004 Myronyuk M. V. |
| spellingShingle | Myronyuk, M. V. Миронюк, М. В. On the Skitovich-Darmois Theorem on Abelian Groups |
| title | On the Skitovich-Darmois Theorem on Abelian Groups |
| title_alt | До теореми Скитовича- Дармуа па абелевих групах |
| title_full | On the Skitovich-Darmois Theorem on Abelian Groups |
| title_fullStr | On the Skitovich-Darmois Theorem on Abelian Groups |
| title_full_unstemmed | On the Skitovich-Darmois Theorem on Abelian Groups |
| title_short | On the Skitovich-Darmois Theorem on Abelian Groups |
| title_sort | on the skitovich-darmois theorem on abelian groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3847 |
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