Definition
Probability Space
A probability space is a triple $(\Omega, \mathcal{F}, \mathbb{P})$ where:
- $(\Omega, \mathcal{F})$ is a measurable space (Definition~Sigma-Algebra), with $\Omega$ the sample space.
- $\mathbb{P} : \mathcal{F} \to [0,1]$ is a probability measure: $\mathbb{P}(\Omega) = 1$, and for pairwise disjoint $A_1, A_2, \ldots \in \mathcal{F}$, \[ \mathbb{P}\!\left(\bigcup_{n=1}^\infty A_n\right) = \sum_{n=1}^\infty \mathbb{P}(A_n). \]
Depends on
Used in
Dependency Graph
flowchart LR
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ndf8f0995["Sigma-Algebra"]
nbbb6ebd1["Probability Space"]:::current
n3eb4aae1["Random Variable"]
n699b1d18["Independence"]
n0729b6b7["Measure Space"]
nccabff62["Stochastic Process"]
ne6452d7c["Filtration and Adapted Process"]
n72af8021["Standard Brownian Motion"]
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click ndf8f0995 "../objects/df8f0995.html" "_self"
click n3eb4aae1 "../objects/3eb4aae1.html" "_self"
click n699b1d18 "../objects/699b1d18.html" "_self"
click n0729b6b7 "../objects/0729b6b7.html" "_self"
click nccabff62 "../objects/ccabff62.html" "_self"
click ne6452d7c "../objects/e6452d7c.html" "_self"
click n72af8021 "../objects/72af8021.html" "_self"