What I took CCC as actually meaning was that the differences converge-in-the-usual-sense to zero, or equivalently that one can make them small enough by waiting long enough. That’s straightforwardly true because if the diameter of your region is D then after n steps your average can’t move by more than D/n per step.
Just to confirm—yes, that’s what I’d meant. Which it trivially true, yes; that is why I couldn’t understand why entirelyuseless was attaching any special significance to it.
Just to confirm—yes, that’s what I’d meant. Which it trivially true, yes; that is why I couldn’t understand why entirelyuseless was attaching any special significance to it.