  We prove a version of the well-known Denjoy-Ahlfors theorem about the number
of asymptotic values of an entire function for properly immersed minimal
surfaces of arbitrary codimension in R^N. The finiteness of the number of ends
is proved for minimal submanifolds with finite projective volume. We show, as a
corollary, that a minimal surface of codimensionn meeting any n-plane passing
through the origin in at most k points has no more c(n,N)k ends.
