Metric Boolean algebras and constructive measure theory

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• 作者：Thierry Coquand and Erik Palmgren
• 刊名：Archive for Mathematical Logic
• 出版年：2002
• 出版时间：October 2002
• 年：2002
• 卷：41
• 期：7
• 页码：687-704
• 全文大小：142 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Logic and Foundations
  Mathematics
  Algebra
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0665

文摘

 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.