There's the concept of a vocabulary growth curve. It shows the number of words occurring once as a function of the amount of text, e.g., how much new words in the first 1000 words? how much in first 2000 words? etc.
But is there a good way to boil that down to a single metric? (i.e., can we parametrize these curves with a single value?)
I wouldn't know off the top of my head, but the concept was introduced by Harold Baayen. There are free PDFs online of his with lots of interesting quantitative techniques.
The idea makes sense, but I'm unclear on how to actually measure it in a way that's normalized by page count.