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arXiv · 2408.13911

Lebesgue integration on $\sigma$-locales: simple functions

Raquel Bernardes
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Abstract

This paper presents a point-free version of the Lebesgue integral for simple functions on $\sigma$-locales. It describes the integral with respect to a measure defined on the coframe of all $\sigma$-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.

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Raquel Bernardes. 2024-08-25. Lebesgue integration on $\sigma$-locales: simple functions. https://arxiv.org/abs/2408.13911

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