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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13911 |
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Table of Contents:
- This paper presents a point-free version of the Lebesgue integral for simple functions on $σ$-locales. It describes the integral with respect to a measure defined on the coframe of all $σ$-sublocales, moving beyond the constraints of Boolean algebras. It also extends the notion of integrable function, usually reserved for measurable functions, to localic general functions.