Sample Space is Union of All Distinct Simple Events

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Let $\EE$ be an experiment.

Let $\Omega$ denote the sample space of $\EE$.

Then $\Omega$ is the union of the set of simple events in $\EE$.


By Set is Subset of Itself:

$\Omega \subseteq \Omega$

That is, $\Omega$ is itself an event in $\EE$.

The result as an application of Non-Trivial Event is Union of Simple Events.