Signed measure

Summary

A signed measure is a countably additive set function on a σ-algebra that may take negative values. It models quantities such as electric charge, which can be positive in some regions and negative in others. Every signed measure is the difference of two ordinary measures, one of them finite. Signed measures appear as differences of measures, as integrals $E \mapsto \int_E f \, d\mu$ of integrable functions, and as elements of dual spaces of function spaces.