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Definition D3649
Random unsigned basic measure

Let $P = (\Omega, \mathcal{F}_{\Omega}, \mathbb{P})$ be a D1159: Probability space.
Let $M = (\Xi, \mathcal{F}_{\Xi})$ be a D1108: Measurable space.
An D4361: Unsigned basic function $\mu : \Omega \times \mathcal{F}_{\Xi} \to [0, \infty]$ is a random unsigned basic measure on $M$ with respect to $P$ if and only if
 (1) For every $E \in \mathcal{F}_{\Xi}$, the D4361: Unsigned basic function $\Omega \to [0, \infty]$ given by $\omega \to \mu(\omega, E)$ is a D4381: Random basic number on $P$ (2) For every $\omega \in \Omega$, the D4361: Unsigned basic function $\mathcal{F}_{\Xi} \to [0, \infty]$ given by $E \mapsto \mu(\omega, E)$ is an D85: Unsigned basic measure on $M$
Children
 ▶ D3650: Random probability measure