Soft Carath\'{e}odory extension Theorem and Soft Outer Measure

Abstract

Molodsov defined the concept of a soft set, which is widely used when drawing conclusionsif we have unclear, incomplete and imprecise information. Soft set theory became an interest of many researchers who defined new concepts such as soft measure, soft $\sigma$-algebra, soft measure, soft outer measure, soft content, etc. In this paper, it was shown that with a certain extension, we can construct a soft measure on the obtained soft $\sigma$-algebra starting from a soft premeasure on a soft semiring.