Lebesgue integration on $σ$-locales: simple functions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916369526685696 |
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| author | Bernardes, Raquel |
| author_facet | Bernardes, Raquel |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lebesgue integration on $σ$-locales: simple functions Bernardes, Raquel Functional Analysis Category Theory 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. |
| title | Lebesgue integration on $σ$-locales: simple functions |
| topic | Functional Analysis Category Theory |
| url | https://arxiv.org/abs/2408.13911 |