On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences
In 2003 Bartoszyński and Halbeisen published the results on various equivalences of Kuratowski and Banach theorem from 1929 concerning some aspect of measure theory. They showed that the existence of the so called BK-matrix related to Banach and Kuratowski theorem is equivalent to the existence of a...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-07-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2018-0066 |
| _version_ | 1819290998510977024 |
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| author | Jureczko Joanna |
| author_facet | Jureczko Joanna |
| author_sort | Jureczko Joanna |
| collection | DOAJ |
| description | In 2003 Bartoszyński and Halbeisen published the results on various equivalences of Kuratowski and Banach theorem from 1929 concerning some aspect of measure theory. They showed that the existence of the so called BK-matrix related to Banach and Kuratowski theorem is equivalent to the existence of a K-Lusin set of cardinality continuum. On the other hand, in 1965 Efimov introduced the strong sequences method and using this method proved some well-known theorems in dyadic spaces. The goal of this paper is to show that the existence of such a K-Lusin set is equivalent to the existence of strong sequences of the same cardinality. Some applications of this results are also shown. |
| first_indexed | 2024-12-24T03:31:39Z |
| format | Article |
| id | doaj.art-c94dfeed2109423faf102c2ff406cc2b |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-24T03:31:39Z |
| publishDate | 2018-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-c94dfeed2109423faf102c2ff406cc2b2022-12-21T17:17:11ZengDe GruyterOpen Mathematics2391-54552018-07-0116172472910.1515/math-2018-0066math-2018-0066On Banach and Kuratowski Theorem, K-Lusin sets and strong sequencesJureczko Joanna0Wrocław University of Science and Technology, Wrocław, PolandIn 2003 Bartoszyński and Halbeisen published the results on various equivalences of Kuratowski and Banach theorem from 1929 concerning some aspect of measure theory. They showed that the existence of the so called BK-matrix related to Banach and Kuratowski theorem is equivalent to the existence of a K-Lusin set of cardinality continuum. On the other hand, in 1965 Efimov introduced the strong sequences method and using this method proved some well-known theorems in dyadic spaces. The goal of this paper is to show that the existence of such a K-Lusin set is equivalent to the existence of strong sequences of the same cardinality. Some applications of this results are also shown.https://doi.org/10.1515/math-2018-0066gchconsistency resultsbk-matrixlusin setstrong sequences03e0503e1003e2003e35 |
| spellingShingle | Jureczko Joanna On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences Open Mathematics gch consistency results bk-matrix lusin set strong sequences 03e05 03e10 03e20 03e35 |
| title | On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences |
| title_full | On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences |
| title_fullStr | On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences |
| title_full_unstemmed | On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences |
| title_short | On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences |
| title_sort | on banach and kuratowski theorem k lusin sets and strong sequences |
| topic | gch consistency results bk-matrix lusin set strong sequences 03e05 03e10 03e20 03e35 |
| url | https://doi.org/10.1515/math-2018-0066 |
| work_keys_str_mv | AT jureczkojoanna onbanachandkuratowskitheoremklusinsetsandstrongsequences |