Extending Fubini Measures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915696711041024 |
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| author | Dries, Lou van den |
| author_facet | Dries, Lou van den |
| contents | Let $C\subseteq M$ be stably embedded in a structure $\cM=(M;\dots)$. We consider {\em Fubini measures} on the subcategory $\Def(C)$ of the category $\Def(\cM)$ of definable sets in $\cM$, with ``Fubini" signaling good behaviour in definable families. We show that such a Fubini measure extends uniquely to the larger subcategory of $\Def(\cM)$ whose objects are the sets that are ``fiberable over $C$". In cases of interest ``fiberable over $C$" coincides with ``co-analyzable relative to $C$." This applies in particular to the differential field $\T$ of transseries with $C=\R$, and to differentially closed fields with constant field $C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Fubini Measures Dries, Lou van den Logic 03C60 Let $C\subseteq M$ be stably embedded in a structure $\cM=(M;\dots)$. We consider {\em Fubini measures} on the subcategory $\Def(C)$ of the category $\Def(\cM)$ of definable sets in $\cM$, with ``Fubini" signaling good behaviour in definable families. We show that such a Fubini measure extends uniquely to the larger subcategory of $\Def(\cM)$ whose objects are the sets that are ``fiberable over $C$". In cases of interest ``fiberable over $C$" coincides with ``co-analyzable relative to $C$." This applies in particular to the differential field $\T$ of transseries with $C=\R$, and to differentially closed fields with constant field $C$. |
| title | Extending Fubini Measures |
| topic | Logic 03C60 |
| url | https://arxiv.org/abs/2512.22662 |