= Usual conditions for a filtration
= Usual hypotheses for a filtration
{synonym}
The usual conditions are completeness and <right-continuous function>[right continuity] of a <filtration>: $\mathcal F_0$ contains all subsets of null <events> in the ambient <probability space>, and $\mathcal F_t=\bigcap_{s>t}\mathcal F_s$. They allow the standard continuous-time <martingale>, <stopping time> and <stochastic integral>[stochastic integration] theorems to be used without repeated augmentation qualifications. An <absolute continuity of measures> change preserves old null sets but can introduce new ones; the usual completion under the new measure may therefore be understood when needed.
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