Canonical model of an independent and identically distributed sequence
= Canonical model of an independent and identically distributed sequence
= Canonical model of an iid sequence
{synonym}
For a probability law $\nu$ on $E$, take the sequence space $E^{\mathbb N}$ with <product measure> $\nu^{\otimes\mathbb N}$. The coordinate maps are an <independent and identically distributed random variables>[independent and identically distributed sequence] with common law $\nu$, and they generate the product <sigma-algebra>.