= Probability space
{title2=$(\Omega,\mathcal F,\mathbb P)$}
{wiki}
A probability space is a <measure space> $(\Omega,\mathcal F,\mathbb P)$ whose total <measure> is one. The <sample space> $\Omega$ contains the elementary outcomes; the <sigma-algebra> $\mathcal F$ contains the <events> to which the model assigns <probabilities>; the <probability measure> $\mathbb P$ supplies those values. The <sigma-algebra> lets us combine observable questions using <complements> and countable <unions> while remaining within the model.
For two independent uniform dice, take $\Omega=\{1,\ldots,6\}^2$, $\mathcal F=\mathcal P(\Omega)$, and give each ordered pair mass $1/36$. A <random variable> might record the sum, the larger result, or whether both results are <even integers>. These are different <functions> on the same <sample space>, rather than different elementary experiments. A <probability distribution> records the mass of the values of one such <random variable> and can forget information retained by the full <probability space>.
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