Integration of mappings of half-ordered rings
Lebesgue type integrals of mappings f: E → X, where X is a semiordered ring and E ⊂R, over a measure with values lying in X are studied. Usual properties of the integral are proved, including theorems on limits under the integral as well as those on absolute continuity and complete additivity of the...
Saved in:
| Date: | 1992 |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7897 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512809251504128 |
|---|---|
| author | Sobolev , V. I. Shcherbin , V. M. Соболев , В. И. Щербин , В. М. |
| author_facet | Sobolev , V. I. Shcherbin , V. M. Соболев , В. И. Щербин , В. М. |
| author_sort | Sobolev , V. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-10-26T11:41:49Z |
| description | Lebesgue type integrals of mappings f: E → X, where X is a semiordered ring and E ⊂R, over a measure with values lying in X are studied. Usual properties of the integral are proved, including theorems on limits under the integral as well as those on absolute continuity and complete additivity of the (u, v)-integral. A theorem on the existence of a solution of a differential equation with (u, v)-derivatives is proved. |
| first_indexed | 2026-03-24T03:34:41Z |
| format | Article |
| fulltext |
0547-1
0548
0549
0550
0551
0552
0553
0554
0555
|
| id | umjimathkievua-article-7897 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:34:41Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e1/78f1a355dca08f9245072a9eba4047e1.pdf |
| spelling | umjimathkievua-article-78972023-10-26T11:41:49Z Integration of mappings of half-ordered rings Об интегрировании отображений полуупорядоченных колец Sobolev , V. I. Shcherbin , V. M. Соболев , В. И. Щербин , В. М. Lebesgue type integrals of mappings f: E → X, where X is a semiordered ring and E ⊂R, over a measure with values lying in X are studied. Usual properties of the integral are proved, including theorems on limits under the integral as well as those on absolute continuity and complete additivity of the (u, v)-integral. A theorem on the existence of a solution of a differential equation with (u, v)-derivatives is proved. Рассматриваются интегралы лебеговского типа отображений f: E→X, где X — полуупорядоченное кольцо, E⸦R, по мере со значениями, принадлежащие X. Доказываются обычные свойства интеграла, в том числе теоремы о предельном переходе под знаком интеграла, об абсолютной непрерывности и полной аддитивности (u, v)-интеграла. Доказывается теорема о существовании решения дифференциального уравнения с (u, v)-производными. Розглядаються інтеграли лебегівського типу відображень f: E→X, де X — напівупоряд-коване кільце, E⸦R, за мірою зі значеннями, що належать X. Доводяться звичайні властивості інтегралу, в тому числі теореми про граничний перехід під знаком інтегралу, про абсолютну неперервність і повну адитивність (u, v)-інтегралу. Доводиться теорема про існування розв’язку диференціального рівняння з (u, v)-похідними. Institute of Mathematics, NAS of Ukraine 1992-04-17 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7897 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 4 (1992); 547-555 Український математичний журнал; Том 44 № 4 (1992); 547-555 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7897/9517 Copyright (c) 1992 V. I. Sobolev , V. M. Shcherbin |
| spellingShingle | Sobolev , V. I. Shcherbin , V. M. Соболев , В. И. Щербин , В. М. Integration of mappings of half-ordered rings |
| title | Integration of mappings of half-ordered rings |
| title_alt | Об интегрировании отображений полуупорядоченных колец |
| title_full | Integration of mappings of half-ordered rings |
| title_fullStr | Integration of mappings of half-ordered rings |
| title_full_unstemmed | Integration of mappings of half-ordered rings |
| title_short | Integration of mappings of half-ordered rings |
| title_sort | integration of mappings of half-ordered rings |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7897 |
| work_keys_str_mv | AT sobolevvi integrationofmappingsofhalforderedrings AT shcherbinvm integrationofmappingsofhalforderedrings AT sobolevvi integrationofmappingsofhalforderedrings AT ŝerbinvm integrationofmappingsofhalforderedrings AT sobolevvi obintegrirovaniiotobraženijpoluuporâdočennyhkolec AT shcherbinvm obintegrirovaniiotobraženijpoluuporâdočennyhkolec AT sobolevvi obintegrirovaniiotobraženijpoluuporâdočennyhkolec AT ŝerbinvm obintegrirovaniiotobraženijpoluuporâdočennyhkolec |