Let P be a hereditary property of words, i.e., aninfinite class of finite words such that every subword (block) ofa word belonging to P is also in P.Extending the classical Morse-Hedlund theorem, we show thateither P contains at least n+1 words of lengthn for every n or, for some N, it contains at most N words of lengthn for every n. More importantly, we prove the following quantitativeextension of this result: if Phas m ≤ n words of length n then, for every k ≥ n + m, it containsat most ⌈(m + 1)/2⌉⌈(m + 1)/2⌈ words of length k.
