  When considering stochastic integration and the theory of stochastic
differential equations, P. Protter's textbook \cite{protter} undoubtedly is a
main piece of standard literature. Not only is it well-written, but it also
contains various profound results regarding these fields. Unfortunately,
Theorem 12 of Chapter V, which presents an equivalence to uniform convergence
on compacts in probability, is found to be incorrect. Given that numerous
important results rely on this theorem, this paper aims to present a corrected
version of it.
