Definition:Complete Set of Events
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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