Families of Sets in Constructive Measure Theory
Logic
2022-07-11 v1
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 -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.
Keywords
Cite
@article{arxiv.2207.04000,
title = {Families of Sets in Constructive Measure Theory},
author = {Max Zeuner},
journal= {arXiv preprint arXiv:2207.04000},
year = {2022}
}