Definition:Event/Occurrence/Intersection

Definition
Let the probability space of an experiment $\EE$ be $\struct {\Omega, \Sigma, \Pr}$.

Let $A, B \in \Sigma$ be events, so that $A \subseteq \Omega$ and $B \subseteq \Omega$.

Let the outcome of the experiment be $\omega \in \Omega$.

Let $\omega \in A \cap B$, where $A \cap B$ denotes the intersection of $A$ and $B$.

Then both $A$ and $B$ occur.

Also denoted as
Some sources denote the occurrence of both $A$ and $B$ as $A B$.

Also see

 * Definition:Union of Events
 * Definition:Difference of Events
 * Definition:Symmetric Difference of Events


 * Definition:Disjoint Events
 * Definition:Complementary Event