Yes, that's right. The growth over any finite window, if you partition it into smaller windows, is the sum of the growth within each partition. Draw enough

Yes, that's right. The growth over any finite window, if you partition it into smaller windows, is the sum of the growth within each partition. Draw enough pictures and you'll develop the intuition that, if you keep partitioning smaller and smaller, you'll reach a point where the average growth rate across a partition is never going to change very much by subpartitioning further. If instantaneous growth rate is going to be defined at all, it has to be very close to the average rate over that tiny interval, no?