On pathwise quadratic variation for cadlag functions

We revisit H. Follmer's concept of quadratic variation of a cadlag function
along a sequence of time partitions and discuss its relation with the Skorokhod
topology. We show that in order to obtain a robust notion of pathwise quadratic
variation applicable to sample paths of cadlag processes, one must reformulate
the definition of pathwise quadratic variation as a limit in Skorokhod topology
of discrete approximations along the partition. The definition then simplifies
and one obtains the Lebesgue decomposition of the pathwise quadratic variation
as a result, rather than requiring it as an extra condition.