Definition:Event/Occurrence/Difference

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 $\omega \in A \setminus B$, where $A \setminus B$ denotes the difference of $A$ and $B$.

Then $A$ occurs but $B$ does not occur.

Also see

• Definition:Union of Events
• Definition:Intersection of Events
• Definition:Symmetric Difference of Events

• Definition:Disjoint Events
• Definition:Complementary Event

Sources

• 1968: A.A. Sveshnikov: Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions (translated by Richard A. Silverman) ... (previous) ... (next): $\text I$: Random Events: $1$. Relations among Random Events