Elementary Properties of Probability Measure
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Theorem
Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.
The probability measure $\Pr$ of $\EE$ has the following properties:
Probability of Empty Event is Zero
- $\map \Pr \O = 0$
Probability of Event not Occurring
- $\forall A \in \Sigma: \map \Pr {\Omega \setminus A} = 1 - \map \Pr A$
Probability Measure is Monotone
Let $A, B \in \Sigma$ such that $A \subseteq B$.
Then:
- $\map \Pr A \le \map \Pr B$