Measure and Integration: Integral representations of isotone functionals
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The present article is another continuation of the recent book of the author  on measure and integration (cited as MI). The subsequent expository paper  (cited as MI0) summarized the essentials, and went on to attain a standpoint which permits the competent evaluation of the traditional extension theories named after Daniell-Stone and Bourbaki, that is of those which start with certain isotone linear functionals. To this end the paper described without proof some further developments. The present article and its predecessor  (cited as MI1) have the aim to elaborate these new developments in adequate contexts. While the previous one dealt with the measure-theoretic aspects proper as described in MI0 sections 1 and 4, the topic this time are certain isotone functionals and their integral representations. We shall elaborate the inner type development of MI sections 14 and 15 into parallel outer and inner representation theories, as formulated in MI0 section 3 as the decisive point for the purpose of that paper.
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