Metric Boolean algebras and constructive measure theory

被引:0
作者
Thierry Coquand
Erik Palmgren
机构
[1] Department of Computer Science,
[2] Chalmers University of Technology and Gothenburg University,undefined
[3] SE-412 96 Göteborg,undefined
[4] Sweden. e-mail: coquand@cs.chalmers.se,undefined
[5] Department of Mathematics,undefined
[6] Uppsala University,undefined
[7] P.O. Box 480,undefined
[8] SE-751 06 Uppsala,undefined
[9] Sweden. e-mail: palmgren@math.uu.se,undefined
来源
Archive for Mathematical Logic | 2002年 / 41卷
关键词
Lebesgue Measure; Boolean Algebra; Measure Theory; Unit Interval; Borel Subset;
D O I
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学科分类号
摘要
 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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页码:687 / 704
页数:17
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