The Range of a Module Measure Defined on an Effect Algebra

Abstract

Effect algebras are the main object of study in quantum mechanics. Module measures are those measures defined on an effect algebra with values on a topological module. Let R be a topological ring and M a topological R-module. Let L be an effect algebra. The range of a module measure μ:L→M is studied. Among other results, we prove that if L is an sRDP σ-effect algebra with a natural basis and μ:L→R is a countably additive measure, then μ has bounded variation.