ABSTRACT
Let X be a set, R be a sigma-algebra of measurable subsets, P be a probability distribution defined for all elements of R, and S be some system of measurable sets A ∈ X . Let Xl = {x1, x2, . . . xl} be an independent sequence, taken from X with distribution P . Two sets A1 and A2 are undifferentiable on the sequence, if and only if
∀i = 1 . . . l, xi ∈ A1 ⇐⇒ xi ∈ A2 . Now we define ∆S(Xl) as the number of classes of sets A ∈ S, undifferentiable on Xl. If
max(log2∆ S(Xl)) ≡ l, we say that the system S has infinite VC dimension.
