Metric Boolean algebras and constructive measure theory

@article{Coquand2002MetricBA,
  title={Metric Boolean algebras and constructive measure theory},
  author={Thierry Coquand and Erik Palmgren},
  journal={Archive for Mathematical Logic},
  year={2002},
  volume={41},
  pages={687-704}
}
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… 

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