Hello, I'm just trying to make it clear that what a finite strategic game is.

The definition of it in my book has this form:

Let G be a strategic game. We say that G is a finite game if, for each player i, |A_{i}|<∞, where A_{i}is the strategy set of player i.

If I let A_{i}be a subset of R^{n}, does |A_{i}| mean the measure of A_{i}in R^{n}?

For instance, if A_{i}=[0,1], an interval of R for all i, then is G a finite game?