On the methods of reduction of some types of Marczewski-Burstin measurable functions to continuous functions on products of perfect sets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912614338002944 |
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| author | Hołubowski, Waldemar Kusiński, Sławomir |
| author_facet | Hołubowski, Waldemar Kusiński, Sławomir |
| contents | In this paper, we introduce product-wise generalizations of certain Marczewski-Burstin bases, including sets with the (s)-property and completely Ramsey sets. For each of these families, we establish analogs of the classical Luzin and Eggleston theorems, showing that functions measurable with respect to these families can be reduced to continuous functions on products of perfect sets. Furthermore, we provide a method for reducilng sequences of such functions to continuity, which allows us to generalize Laver's extension of Halpern-Läuchli and Harrington theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the methods of reduction of some types of Marczewski-Burstin measurable functions to continuous functions on products of perfect sets Hołubowski, Waldemar Kusiński, Sławomir Combinatorics Logic Primary 03E15 Secondary 28A05 06A07 54H05 54B10 In this paper, we introduce product-wise generalizations of certain Marczewski-Burstin bases, including sets with the (s)-property and completely Ramsey sets. For each of these families, we establish analogs of the classical Luzin and Eggleston theorems, showing that functions measurable with respect to these families can be reduced to continuous functions on products of perfect sets. Furthermore, we provide a method for reducilng sequences of such functions to continuity, which allows us to generalize Laver's extension of Halpern-Läuchli and Harrington theorems. |
| title | On the methods of reduction of some types of Marczewski-Burstin measurable functions to continuous functions on products of perfect sets |
| topic | Combinatorics Logic Primary 03E15 Secondary 28A05 06A07 54H05 54B10 |
| url | https://arxiv.org/abs/2506.06458 |