Definition 3.1.2 (Previsible Path Functional).label Let $C([0, \infty); \real^{d})$ be the space of $\real^{d}$-valued continuous functions on $[0, \infty)$, equipped with the topology of uniform convergence. For each $t \ge 0$, let

and $\mathscr{J}_{C([0, \infty); \real^d)}$ be the previsible $\sigma$-algebra on $(0, \infty) \times C([0, \infty); \real^{d})$, then a previsible path functional is a $\mathscr{J}$-measurable mapping on $(0, \infty) \times C([0, \infty); \real^{d})$.