The Derivative of a Constructible Function is Constructible
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914507097374720 |
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| author | Kaiser, Tobias |
| author_facet | Kaiser, Tobias |
| contents | The notion of constructible functions in the setting of tame real geometry has been introduced by Cluckers and Dan Miller in their work on parametric integration of globally subanalytic functions. A function on a globally subanalytic set is called constructible if it is a finite sum of finite products of globally subanalytic functions and the logarithm of positive globally subanalytic functions. We show that the class of constructible functions is stable under taking derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Derivative of a Constructible Function is Constructible Kaiser, Tobias Logic Algebraic Geometry Complex Variables 03C64, 14P15, 26A09, 32B20 The notion of constructible functions in the setting of tame real geometry has been introduced by Cluckers and Dan Miller in their work on parametric integration of globally subanalytic functions. A function on a globally subanalytic set is called constructible if it is a finite sum of finite products of globally subanalytic functions and the logarithm of positive globally subanalytic functions. We show that the class of constructible functions is stable under taking derivatives. |
| title | The Derivative of a Constructible Function is Constructible |
| topic | Logic Algebraic Geometry Complex Variables 03C64, 14P15, 26A09, 32B20 |
| url | https://arxiv.org/abs/2508.02517 |