Sigma additivity

In mathematics, additivity and sigma additivity (also called countable additivity) of a function defined on subsets of a given set are abstractions of the intuitive properties of size (length, area, volume) of a set.

Let ${\displaystyle \mu }$ be a function defined on an algebra of sets ${\displaystyle \scriptstyle {\mathcal {A}}}$ with values in [−∞, +∞] (see the extended real number line). The function ${\displaystyle \mu }$ is called additive, or finitely additive, if, whenever A and B are disjoint sets in ${\displaystyle \scriptstyle {\mathcal {A}}}$, one has

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