Atoms and Dobrakov submeasures in effect algebras

The present paper deals with the study of the notion of Dobrakov submeasure m defined on an effect algebra L with values in [0,∞). We have established the equivalence of the following three properties for a Dobrakov submeasure m defined on a σ-complete effect algebra L: (i) m is atomless, (ii) m has Saks property, (iii) m has Darboux property. We have also studied the concept of an atom of a function μ defined on an effect algebra L with values in [0,∞) and finally, we have proved for a monotone, m-continuous and semicontinuous function μ defined on a σ-complete effect algebra L that, μ is non-atomic if and only if μ is atomless.