Limitedness ...the quality or state of being limited.
-They found that males are more likely than females to feel stressed 'overwhelmed' or 'depressed', and they attributed this to limitedness of men's social networks.
-In recognizing her nothingness, St. Theresa was acknowledging the infinite distance between the boundlessness of God and the limitedness of any creature.
-The limitedness of land results in the price of grain being determined by the conditions of production, not on the average land, but on the worst land under cultivation.
I wouldn't call this the most commonly used word in the dictionary, but if you insist on the use of only one word it describes limitation in general.
Actually, neither finite nor limitedness is the exact word you are looking for. The word that can be used in an active sense or a passive sense to describe either ability or property would be LIMITATION.
limitation...the act of limiting.
The proper limitation of mathematics to the realm of matter
limitation....the quality or state of being limited: limitedness
The limitation of the human intellect