New Generalizations of the Scorza-Dragoni Theorem
We consider Carathéodory functions f : T × X → Y, where T is a topological space with regular σ-finite measure, the spaces X and Y are metrizable and separable, and X is locally compact. We show that every function of this sort possesses the Scorza-Dragoni property. A similar result is also establis...
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| Datum: | 2000 |
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Institute of Mathematics, NAS of Ukraine
2000
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| author | Gaidukevich, O. L. Maslyuchenko, V. K. Гайдукевич, О. І. Маслюченко, В. К. |
| author_facet | Gaidukevich, O. L. Maslyuchenko, V. K. Гайдукевич, О. І. Маслюченко, В. К. |
| author_sort | Gaidukevich, O. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:30:08Z |
| description | We consider Carathéodory functions f : T × X → Y, where T is a topological space with regular σ-finite measure, the spaces X and Y are metrizable and separable, and X is locally compact. We show that every function of this sort possesses the Scorza-Dragoni property. A similar result is also established in the case where the space T is locally compact and X = ℝ∞. |
| first_indexed | 2026-03-24T02:59:51Z |
| format | Article |
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| id | umjimathkievua-article-4487 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:59:51Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/fb/141c5d44d6285be598877b92909170fb.pdf |
| spelling | umjimathkievua-article-44872020-03-18T20:30:08Z New Generalizations of the Scorza-Dragoni Theorem Нові узагальнення теореми Скорца-Драгоні Gaidukevich, O. L. Maslyuchenko, V. K. Гайдукевич, О. І. Маслюченко, В. К. We consider Carathéodory functions f : T × X → Y, where T is a topological space with regular σ-finite measure, the spaces X and Y are metrizable and separable, and X is locally compact. We show that every function of this sort possesses the Scorza-Dragoni property. A similar result is also established in the case where the space T is locally compact and X = ℝ∞. Показано, що кожна функція Каратеодорі $f : T × X → Y$ —де $Т$ — топологічний простір з регулярною $σ$-скінченною мірою, простори $X$ і $Y$ — метризовні і сепарабельні, $X$ — локально компактний, має властивість Скорца-Драгоні. Аналогічний результат одержано, коли простір $T$ — локально компактний і $X = ℝ^{∞}$ Institute of Mathematics, NAS of Ukraine 2000-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4487 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 7 (2000); 881-888 Український математичний журнал; Том 52 № 7 (2000); 881-888 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4487/5678 https://umj.imath.kiev.ua/index.php/umj/article/view/4487/5679 Copyright (c) 2000 Gaidukevich O. L.; Maslyuchenko V. K. |
| spellingShingle | Gaidukevich, O. L. Maslyuchenko, V. K. Гайдукевич, О. І. Маслюченко, В. К. New Generalizations of the Scorza-Dragoni Theorem |
| title | New Generalizations of the Scorza-Dragoni Theorem |
| title_alt | Нові узагальнення теореми Скорца-Драгоні |
| title_full | New Generalizations of the Scorza-Dragoni Theorem |
| title_fullStr | New Generalizations of the Scorza-Dragoni Theorem |
| title_full_unstemmed | New Generalizations of the Scorza-Dragoni Theorem |
| title_short | New Generalizations of the Scorza-Dragoni Theorem |
| title_sort | new generalizations of the scorza-dragoni theorem |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4487 |
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