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Mathematics > Logic

arXiv:2207.04000 (math)
[Submitted on 8 Jul 2022]

Title:Families of Sets in Constructive Measure Theory

Authors:Max Zeuner
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Abstract:We present the first steps of a predicative reconstruction of the constructive Bishop-Cheng measure theory. Working in a semi-formal elaboration of Bishop's set theory and invoking the notion of a set-indexed family of subsets (of a given set), we arrive at notions of a pre-integration space and of a pre-measure space. We then construct the pre-integration space of simple functions associated to a pre-measure space and the $L^1$-completion of a pre-integration space. Unlike the standard presentation of Bishop-Cheng measure theory, our development is completely predicative and avoids the axiom of countable choice.
Subjects: Logic (math.LO)
Cite as: arXiv:2207.04000 [math.LO]
  (or arXiv:2207.04000v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.2207.04000

Submission history

From: Max Zeuner [view email]
[v1] Fri, 8 Jul 2022 16:35:05 UTC (36 KB)
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