= Almost sure event
{title2=$\mathbb P(A)=1$}
An almost sure event is a measurable event of probability one. Countable intersections of such events still have probability one, allowing a conclusion to hold simultaneously for countably many parameter choices. Further deterministic reasoning may then extend it to uncountably many parameters, as in <Brownian Hölder regularity> or <nowhere monotonicity of Brownian motion>. An uncountable intersection need not preserve probability one without such additional reasoning.
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