Constructive algebraic integration theory

Annals of Pure and Applied Logic 137 (1-3):380-390 (2006)
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Abstract

For a long time people have been trying to develop probability theory starting from ‘finite’ events rather than collections of infinite events. In this way one can find natural replacements for measurable sets and integrable functions, but measurable functions seemed to be more difficult to find. We present a solution. Moreover, our results are constructive

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10.1016/j.apal.2005.05.031

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Citations of this work

The swap of integral and limit in constructive mathematics.Rudolf Taschner - 2010 - Mathematical Logic Quarterly 56 (5):533-540.
Lebesgue’s dominated convergence theorem in Bishop’s style.Claudio Coen & Enrico Zoli - 2012 - Annals of Pure and Applied Logic 163 (2):140-150.

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References found in this work

Varieties of constructive mathematics.D. S. Bridges & Fred Richman - 1987 - New York: Cambridge University Press. Edited by Fred Richman.
Constructive Analysis.Errett Bishop & Douglas Bridges - 1987 - Journal of Symbolic Logic 52 (4):1047-1048.
Complete metric Boolean algebras.A. N. Kolmogorov - 1995 - Philosophical Studies 77 (1):57 - 66.
Metric Boolean algebras and constructive measure theory.Thierry Coquand & Erik Palmgren - 2002 - Archive for Mathematical Logic 41 (7):687-704.

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