S-finite measure

In measure theory, a branch of mathematics that studies generalized notions of volumes, an s-finite measure is a special type of measure. An s-finite measure is more general than a finite measure, but allows one to generalize certain proofs for finite measures.

The s-finite measures should not be confused with the σ-finite (sigma-finite) measures.

Let ${\displaystyle (X,{\mathcal {A}})}$ be a measurable space and ${\displaystyle \mu }$ a measure on this measurable space. The measure ${\displaystyle \mu }$ is called an s-finite measure, if there are at most countably many finite measures ${\displaystyle \nu _{n}}$ (${\displaystyle n\in \mathbb {N} }$) satisfying

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