It is known that the voltage drop across a capacitor is a continuous function of time. This means that, for each instant t0, we may write:
V(t0-) = V(t0+)
This relationship is very used in the time domain analysis of RC circuits for instance, and it is due to the fact that if V was not continuous, it would mean infinite current across the capacitor, which is not physically possible.
But which is the mathematical proof of that? I remember I saw it on a book but I do not find it any more. I remember that it was a consequence of the relationship i = C dV/dt....