A STUDY OF NON-ATOMIC MEASURES AND INTEGRALS ON EFFECT ALGEBRAS

Abstract

The present paper deals with the study of superior variation $m^{+}$, inferior variation $m^{-}$ and total variation $|m|$ of an extended real-valued function $m$ defined on an effect algebra $L.$ Various properties in the context of functions $m^{+}$, $m^{-}$ and $|m|$ are also established. Using the notion of an atom of a real-valued function, we have proved Intermediate value theorem for a non-atomic function $m$ defined on a $D$-lattice $L$ under suitable conditions. Finally, the notion of the integral for a bounded, real-valued function with respect to a measure on effect algebras with Reisz decomposition property is introduced and studied.