A Soft Dynkin System

Abstract

Molodtsov defined the concept of a soft set, which is widely used in inference in case of vague, incomplete and imprecise information. The soft set theory became of interest to many researchers who defined new concepts such as soft measure, soft $\sigma$-algebra, soft premeasure, soft semiring, etc. In this paper, it is shown that starting from a soft premeasure defined on a soft semiring, we obtain a unique soft measure defined on a soft $\sigma$-algebra generated by a soft semiring. The terms soft $\sqcap$-stable, soft monotone class and soft Dynkin system were introduced as a necessary tool for realization.