In this paper we prove that if u: Bn → R, where Bn is the unit ball in Rn, is a monotone function in the Sobolev space W1.p (En), and n - 1 < p ≤ n, then u has nontangential limits at all the points of ∂Bn except possibly on a set of p-capacity zero. The key ingredient in the proof is an extension of a classical theorem of Lindelöf to monotone functions in W1.p (En), n - 1 < p ≤ n.
