Atoms and a Saks Type Decomposition in Effect Algebras
نویسندگان
چکیده
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. AMS Mathematics Subject Classification (2000): 06A11, 28A12, 06C15
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