A computable version of the Daniell–Stone theorem on integration and linear functionals

For every measure μ, the integral 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 for all f∈F. In this paper we prove a computable version of this theorem.