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Probability Space

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Definition
MeasureTheoryProbability

A probability space is a measure space (Ω,F,P)(\Omega,\mathcal{F},P) where: - Ω\Omega is the Sample Space - F\mathcal{F} is the Event Space - PP is a Probability Measure

Let Ω\Omega be a finite or countable, non-empty set. Let p:Ω[0,1]p:\Omega\to[0,1] be any function satisfying ωΩp(ω)=1.\sum_{\omega \in\Omega}p(\omega)=1.Then there is a Probability Space (Ω,F,P)(\Omega,\mathcal{F},\mathbb{P}) for F=2Ω,P(E)=ωEp(ω)\mathcal{F}=2^{\Omega},\mathbb{P}(E)=\sum_{\omega \in E}p(\omega).

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