A Computable Version of the Daniell-Stone Theorem on Integration and Linear Functionals

  • Authors:

  • Yongcheng Wu;Klaus Weihrauch

  • Affiliations:

  • Mathematics Department, Nanking University, Nanking, China;Computer Scienece, Fernuniversität, Hagen, Germany

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2005

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Abstract

For every measure @m, the integral I:f@?@!fd@m is a linear functional on the set of real measurable functions. By the Daniell-Stone theorem, for every abstract integral @L:F-R on a stone vector lattice F of real functions f:@W-R there is a measure @m such that @!fd@m=@L(f) for all f@?F. In this paper we prove a computable version of this theorem.