question re Vapnik's book - "the nature of statistical learning theory"

[Faheem Mitha]

Hi everyone,

I'm writing with a question from Vapnik's book (2nd edn). To answer this,
you'll probably need to have the book handy.

On pg 42, he has

Consider the set of l-dimensional binary vectors

$ q(\alpha) = (Q(z_1, \alpha), \dots, , Q(z_l, \alpha)),   \alpha \in \Lambda$

that one obtains when $\alpha$ takes various values from $\Lambda$. Then
geometrically speaking, $N^{\Lambda}(z_1, \dots, z_l)$ is the number of
different vertices of the $l$-dimensional cube that can be obtained on the
basis of the sample $z_1, \dots, z_l$. and the set of functions $Q(z,
\alpha) \in \Lambda$.

I'm having difficulty parsing the definition of $N^{\Lambda}$. Can anyone
elaborate on what he meant here?

                                                            Thanks, Faheem.