In mathematics, a decomposable measure[1] (also known as a strictly localizable measure) is a measure that is a disjoint union of finite measures. This is a generalization of σ-finite measures, which are the same as those that are a disjoint union of countably many finite measures. There are several theorems in measure theory such as the Radon–Nikodym theorem that are not true for arbitrary measures but are true for σ-finite measures. Several such theorems remain true for the more general class of decomposable measures. This extra generality is not used much as most decomposable measures that occur in practice are σ-finite.



  1. ^ Fremlin 2016, Definition 211E, p. 12.