quality:correction
Semifinite measures

Let X {\displaystyle X} be a set, let A {\displaystyle {\cal {A}}} be a sigma-algebra on X, {\displaystyle X,} and let μ {\displaystyle \mu } be a measure on A. {\displaystyle {\cal {A}}.} We say μ {\displaystyle \mu } is semifinite to mean that for all A ∈ μ pre { + ∞ }, {\displaystyle A\in \mu ^{\text{pre}}\{+\infty \},} P (A) ∩ μ pre (R > 0) ≠ ∅. {\displaystyle {\cal {P}}(A)\cap \mu ^{\text{pre}}(\mathbb {R} _{>0})\neq \emptyset.}

Semifinite measures generalize sigma-finite measures, in such a way that some big theorems of measure theory that hold for sigma-finite but not arbitrary measures can be extended with little modification to hold for semifinite measures. (To-do: add examples of such theorems; cf. the talk page.)