TY  - JOUR
T1  - How to extend Carathéodory's theorem to lattice-valued functionals
AU  - Agbeko, Nutefe Kwami
PY  - 2020
DA  - September
JF  - Results in Nonlinear Analysis
JO  - RNA
PB  - Erdal KARAPINAR
WT  - DergiPark
SN  - 2636-7556
SP  - 117
EP  - 127
VL  - 3
IS  - 3
LA  - en
AB  - 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.
KW  - outer mearsure
KW  - sigma-algebra
KW  - measurable sets
KW  - Hausdorff measure
KW  - Hausdorff dimension
KW  - Caratheodory-type theorem
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UR  - https://dergipark.org.tr/tr/pub/rna/issue//763942
L1  - https://dergipark.org.tr/tr/download/article-file/1187107
ER  -