Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures
We study integrals $∫fdμ$ of real functions over $L_0$-valued measures. We give a definition of convergence of real functions in quasimeasure and, as a special case, in $L_0$-measure. For these types of convergence, we establish conditions of convergence in probability for integrals over $L_0$-value...
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5287 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511503218638848 |
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| author | Radchenko, V. N. Радченко, В. Н. Радченко, В. Н. |
| author_facet | Radchenko, V. N. Радченко, В. Н. Радченко, В. Н. |
| author_sort | Radchenko, V. N. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:29:27Z |
| description | We study integrals $∫fdμ$ of real functions over $L_0$-valued measures. We give a definition of convergence of real functions in quasimeasure and, as a special case, in $L_0$-measure. For these types of convergence, we establish conditions of convergence in probability for integrals over $L_0$-valued measures, which are analogous to the conditions of uniform integrability and to the Lebesgue theorem. |
| first_indexed | 2026-03-24T03:13:55Z |
| format | Article |
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| id | umjimathkievua-article-5287 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:13:55Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/64/fb6894f55f827c4e71ec82fe4619bc64.pdf |
| spelling | umjimathkievua-article-52872020-03-18T21:29:27Z Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures Равномерная интегрируемость и теорема Лебега для сходимости по $L_0$-значным мерам Radchenko, V. N. Радченко, В. Н. Радченко, В. Н. We study integrals $∫fdμ$ of real functions over $L_0$-valued measures. We give a definition of convergence of real functions in quasimeasure and, as a special case, in $L_0$-measure. For these types of convergence, we establish conditions of convergence in probability for integrals over $L_0$-valued measures, which are analogous to the conditions of uniform integrability and to the Lebesgue theorem. Розглядаються інтеграли $∫fdμ$ від дійсних функцій за $L_0$-значними мірами. Дається означення збіжності дійсних функцій за квазімірою та, як частинний випадок, за $L_0$-значною мірою. Для таких видів збіжності одержані умови збіжності за ймовірністю для інтегралів за $L_0$-значними мірами, аналогічні умовам рівномірної інтег ровності та теоремі Лебега. Institute of Mathematics, NAS of Ukraine 1996-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5287 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 6 (1996); 857-860 Український математичний журнал; Том 48 № 6 (1996); 857-860 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5287/7266 https://umj.imath.kiev.ua/index.php/umj/article/view/5287/7267 Copyright (c) 1996 Radchenko V. N. |
| spellingShingle | Radchenko, V. N. Радченко, В. Н. Радченко, В. Н. Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures |
| title | Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures |
| title_alt | Равномерная интегрируемость и теорема Лебега для сходимости по
$L_0$-значным мерам |
| title_full | Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures |
| title_fullStr | Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures |
| title_full_unstemmed | Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures |
| title_short | Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures |
| title_sort | uniform integrabblity and the lebesgue theorem on convergence in $l_0$-valued measures |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5287 |
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