Metric Boolean algebras and constructive measure theory

Archive for Mathematical Logic 41 (7):687-704 (2002)
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Abstract

This work concerns constructive aspects of measure theory. By considering metric completions of Boolean algebras – an approach first suggested by Kolmogorov – one can give a very simple construction of e.g. the Lebesgue measure on the unit interval. The integration spaces of Bishop and Cheng turn out to give examples of such Boolean algebras. We analyse next the notion of Borel subsets. We show that the algebra of such subsets can be characterised in a pointfree and constructive way by an initiality condition. We then use our work to define in a purely inductive way the measure of Borel subsets

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Citations of this work

Constructive algebraic integration theory.Bas Spitters - 2006 - Annals of Pure and Applied Logic 137 (1-3):380-390.

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References found in this work

Foundations of Constructive Analysis.Errett Bishop - 1967 - New York, NY, USA: Mcgraw-Hill.
Complete metric Boolean algebras.A. N. Kolmogorov - 1995 - Philosophical Studies 77 (1):57 - 66.

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