ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Measurable space
Measurable map
Measurable function
Pre-kernel
Measure kernel
Definition D3649
Random unsigned basic measure
Formulation 2
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
Random probability measure