Definition:Event/Occurrence/Equality

Definition

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

Let $A, B \in \Sigma$ be events of $\EE$ such that $A = B$.

Then:

the occurrence of $A$ inevitably brings about the occurrence of $B$

and:

the occurrence of $B$ inevitably brings about the occurrence of $A$.

Also see

• Definition:Impossible 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