Definition:Complete Set of Events

Definition

Let $I$ be an indexing set.

Let $\family {A_i}_{i \mathop \in I}$ be a family of events in a probability space indexed by $I$.

$\family {A_i}_{i \mathop \in I}$ is a complete set of events if and only if:

$\ds \map \Pr {\bigcup_{i \mathop \in I} A_i} = 1$

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