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Definition D85
Unsigned basic measure

Let $M = (X, \mathcal{F})$ be a D1108: Measurable space.
An D4361: Unsigned basic function $\mu : \mathcal{F} \to [0, \infty]$ is an unsigned basic measure on $M$ if and only if
 (1) $$\mu(\emptyset) = 0$$ (2) $$\forall \, E_0, E_1, E_2, \dots \in \mathcal{F} \left( \forall \, n, m \in \mathbb{N} \left( n \neq m \quad \implies \quad E_n \cap E_m = \emptyset \right) \quad \implies \quad \mu \left( \bigcup_{n \in \mathbb{N}} E_n \right) = \sum_{n \in \mathbb{N}} \mu(E_n) \right)$$
Children
 ▶ D2887: Absolutely continuous measure ▶ D1734: Outer measure ▶ D3566: Set of unsigned basic measures ▶ D1731: Submeasure ▶ D3880: Unsigned basic integral measure ▶ D1680: Zero measure