ATOMS AND A SAKS TYPE DECOMPOSITION IN EFFECT ALGEBRAS
Mona Khare, Akhilesh Kumar Singh · 2008
Abstract. The present paper deals with the study of the notion of an atom of a function m defined on an effect algebra L with values in [0, ∞]; a few examples of atoms for null-additive as well as for non-null-additive functions are also given. We have proved a Saks type decomposition theorem for an element a with m(a)> 0 (for a suitable m), which does not contain any atom of m, in a σ-complete effect algebra L. A characterization for a measure µ to be non-atomic (µ is defined on a σ-complete effect algebra with values in [0, ∞]) is established and a result for a non-atomic measure µ is proved, which has resemblance with the Intermediate Value Theorem for continuous functions.