Σ-finite measure

In mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called finite if μ(X) is a finite real number (rather than ∞). The measure μ is called σ-finite if X is the countable union of measurable sets with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure.

A different but related notion is s-finiteness. A measure ${\displaystyle m}$ is s-finite if and only if there exists a sequence of finite measures ${\displaystyle (m_{n})_{n}:m=\sum _{n\in \mathbb {N} }m_{n}}$, that is: m is the countable sum of finite measures.

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