- Results in Nonlinear Analysis
- Vol: 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 : 11 | Download : 11
Publication Date : 2020-09-30
Article Type : Research
Abstract :Substituting in the definition of outer measure the addition with the maximum (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