Elementary outcome
= Elementary outcome
{title2=$\omega\in\Omega$}
An <elementary outcome> is one member of the <sample space>. For the ordered two-toss model, $HT$ is one outcome; it contains both toss results. By contrast, “at least one head” is an <event> containing three outcomes. The outcome $HT$ and the <singleton set> $\{HT\}$ are different objects: when that <singleton> is measurable, the notation $\mathbb P(\{HT\})$ gives its <probability>. In the finite model below, every <subset> is measurable.
The word elementary refers to the chosen level of detail. An outcome can be an <ordered pair>, a sequence, or an entire realization of a <point process>. A <random variable> then extracts a numerical feature of that outcome; the <window count of a point process> is one example.