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Lebesgue Integral in Constructive Analysis

  • Oswald Demuth
Part of the Seminars in Mathematics book series (SM, volume 4)

Abstract

In the present note it is assumed that the reader is acquainted with [1]. 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
$$x_1^1 \vartriangle \,x_1^2 \,\square \,x_2^1 \,\vartriangle \,x_2^2 \,\square \cdots \square \,\,x_n^1 \vartriangle \,x_n^2 ,$$
(1)
where x j 1 , x j 2 are CRN from 0Δ1, such that x j 1 < x j 2 (1 ≤j ≤ n).

Keywords

Natural Number Real Variable Consultant Bureau Present Note Constructive Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    Demuth, O., “On Lebesgue integration in constructive analysis,” Doklady Akad. Nauk SSSR, 160(6): 1239–1241 (1965).Google Scholar

Copyright information

© Consultants Bureau 1969

Authors and Affiliations

  • Oswald Demuth

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