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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.10662 |
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| _version_ | 1866909948814819328 |
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| author | Micheas, Athanasios Christou |
| author_facet | Micheas, Athanasios Christou |
| contents | Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the definition and properties of a new space of functions, which will be called multivariate Taylor measure function space. The proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem Micheas, Athanasios Christou Functional Analysis Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the definition and properties of a new space of functions, which will be called multivariate Taylor measure function space. The proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases. |
| title | The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2508.10662 |