Abstract: Motivated by questions arising in financial mathematics, Dupire introduced a notion of smoothness for functionals of paths and arrived at a generalization of Ito’s formula applicable to functionals which have a pathwise continuous dependence on the trajectories of the underlying process. Work of Cont&Fournie shows that the class of functionals can be significantly extended, for example to include processes like the quadratic variation of semimartingales, etc. We revisit this topic and use old work of Bichteler on pathwise integration to explore another approach to extend the class of functionals. This allows to develop a functional Ito calculus simultaneously under a family of non-dominated probability measures on pathspace.