How to extend Carathéodory`s theorem to lattice-valued functionals

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Results in Nonlinear Analysis
Volume:3 Issue:3
How to extend Carathéodory`s theorem to lattice-valued functionals

How to extend Carathéodory`s theorem to lattice-valued functionals

Authors : Nutefe Kwami AGBEKO

Pages : 117-127

View : 12 | Download : 7

Publication Date : 2020-09-30

Article Type : Research Paper

Abstract :Substituting in the definition of outer measure the addition with the maximum insert ignore into journalissuearticles values(or the supremum, or the join); operation we obtain a new set function called retuo measure. It is proved that every retuo measure is an outer measure. We give necessary and sufficient conditions for a set function to be a retuo measure. Similarly as in the case of outer measure, we propose a way to construct retuo measures. We consider some theoretical applications for constructed pairs of outer and retuo measures in the image of the Hausdorff measure and dimension.
Keywords : outer mearsure, sigma algebra, measurable sets, Hausdorff measure, Hausdorff dimension, Caratheodory type theorem

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