Lebesgue Integral in Constructive Analysis
Part of the Seminars in Mathematics book series (SM, volume 4)
In the present note it is assumed that the reader is acquainted with . We shall understand algorithms to be normal algorithms in the alphabet of constructive real numbers (CRN), extended by the letters Δ, □, β. Let n be a natural number, n ≥ 1. We shall call n-points words of the form x1□x2□...□xn, where all the xi (1 ≤ i ≤ n) are CRN from 0 Δ 1 and we shall call n-segments, words of the form
where x j 1 , x j 2 are CRN from 0Δ1, such that x j 1 < x j 2 (1 ≤j ≤ n).
$$x_1^1 \vartriangle \,x_1^2 \,\square \,x_2^1 \,\vartriangle \,x_2^2 \,\square \cdots \square \,\,x_n^1 \vartriangle \,x_n^2 ,$$
KeywordsNatural Number Real Variable Consultant Bureau Present Note Constructive Theory
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- 1.Demuth, O., “On Lebesgue integration in constructive analysis,” Doklady Akad. Nauk SSSR, 160(6): 1239–1241 (1965).Google Scholar
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