Open AccessA Computable Version of the Daniell-Stone Theorem on Integration and Linear Functionals
Author(s) -
Yongcheng Wu,
Klaus Weihrauch
Publication year - 2005
Publication title -
electronic notes in theoretical computer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.242
H-Index - 60
ISSN - 1571-0661
DOI - 10.1016/j.entcs.2004.06.046
Subject(s) - mathematics , computable analysis , measure (data warehouse) , discrete mathematics , computable function , pure mathematics , computer science , database
For every measure μ, the integral I:f↦∫fdμ is a linear functional on the set of real measurable functions. By the Daniell-Stone theorem, for every abstract integral Λ:F→R on a stone vector lattice F of real functions f:Ω→R there is a measure μ such that ∫fdμ=Λ(f) for all f∈F. In this paper we prove a computable version of this theorem
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