Colocatedness and Lebesgue Integrability

  • Douglas S. Bridges
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)


With reference to Mandelkern’s characterisation of colocated subsets of the line in constructive analysis, we introduce the notion of “strongly colocated set” and find conditions under which such a set is Lebesgue integrable.


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  1. 1.
    Aczel, P., Rathjen, M.: Notes on Constructive Set Theory, Report No. 40, Institut Mittag-Leffler, Royal Swedish Academy of Sciences (2001)Google Scholar
  2. 2.
    Berger, J., Bridges, D.S., Mahalanobis, A.: The anti-Specker property, a Heine–Borel property, and uniform continuity, preprint, University of Canterbury (January 2007)Google Scholar
  3. 3.
    Bishop, E.A.: Foundations of Constructive Analysis, McGraw-Hill, New York (1967)Google Scholar
  4. 4.
    Bishop, E.A., Bridges, D.S.: Constructive Analysis. Springer, Heidelberg (1985)MATHGoogle Scholar
  5. 5.
    Bridges, D.S., Vîţă, L.S.: Techniques of Constructive Analysis, Universitext. Springer, New York (2006)Google Scholar
  6. 6.
    Bridges, D.S., Richman, F.: Varieties of Constructive Mathematics. London Math. Soc. Lecture Notes, vol. 97. Cambridge Univ. Press, Cambridge (1987)Google Scholar
  7. 7.
    Mandelkern, M.: Located sets on the line. Pacific J. Math 95(2), 401–409 (1981)MATHMathSciNetGoogle Scholar
  8. 8.
    Specker, E.: Nicht konstruktiv beweisbare Sätze der Analysis. J. Symb. Logic 14, 145–158 (1949)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Douglas S. Bridges
    • 1
  1. 1.Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800 ChristchurchNew Zealand

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