ON AN ALGEBRAIZATION OF MEASURE THEORY. ABSTRACT SEMIRINGS

Abstract

The concept of a semiring is introduced as a semilattice analogue of a semiring of sets. A detailed study of its embeddability into r-complete Boolean algebras is carried out. Some of its properties which are important from the standpoint of Measure Theory are elucidated. A representation of a semiring by a Semiring of sets is derived. A relation to implicative BCK-algebras is also mentioned.