@article{article_763942, title={How to extend Carathéodory’s theorem to lattice-valued functionals}, journal={Results in Nonlinear Analysis}, volume={3}, pages={117–127}, year={2020}, author={Agbeko, Nutefe Kwami}, keywords={outer mearsure, sigma-algebra, measurable sets, Hausdorff measure, Hausdorff dimension, Caratheodory-type theorem}, 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.}, number={3}, publisher={Erdal KARAPINAR}