Convergence of probability measures on separable banach spaces

The following result follows immediately from a general theorem on the convergence of probability measures on separable Banach spaces: On the space C[0, 1] there exists a norm p(x) equivalent to the ordinary norm such that if ξ₁(t),… ξ_n(t),…and ξ(t) are continuous random processes (0 ≤ t ≤ 1) and for any finite set of points t₁,…, t_k ⊂ [0, 1] the joint distribution of p(ξ_n), ξ_n(t₁),…, ξ_n(t_k) converges to the joint distribution of p(ξ), ξ(t₁),…, ξ(t_k) then ξ_n(t) converges weakly to ξ(t).