On a dyadic approximation of predictable processes of finite variation

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We show that any cadlag predictable process of finite variation is an a.s. limit of elementary predictable processes; it follows that predictable stopping times can be approximated `from below' by predictable stopping times which take finitely many values. We then obtain as corollaries two classical theorems: predictable stopping times are announceable, and an increasing process is predictable iff it is natural.