= Cylinder sigma-algebra
{title2=$\mathcal C$}
= Coordinate sigma-algebra
{synonym}
On a product space $\mathbb R^T$, the <cylinder sigma-algebra> is the smallest <sigma-algebra> making every coordinate projection $x\mapsto x(t)$ measurable. Its generators ask finitely many coordinate questions. Every <event> in it depends on at most countably many coordinates: the collection of countably determined <sets> contains these generators and is closed under complements and countable unions. If $T$ is uncountable, the singleton consisting of the identically zero <function> is not such an <event>. Any countable coordinate test leaves an untested coordinate where a different <function> can be nonzero. Thus coordinate measurability alone need not capture every pathwise question.
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