Nonstandard characterization of convergence in law for D[0,1]-valued random variables

We prove for random variables with values in the space D[0, 1] of cadlag fu nctions - endowed with the supremum metric - that convergence in law is equ ivalent to nonstandard constructions of internal S-cadlag processes, which represent up to an infinitesimal error the limit process. It is not require d that the limit process is concentrated on the space C[0, 1], so that the theory is applicable to a wider class of limit processes as e.g. to Poisson processes or Gaussian processes. If we consider in D[0, 1] the Skorokhod m etric instead of the supremum metric - we obtain a corresponding equivalenc e to constructions of internal processes with S-separated jumps. We apply t hese results to functional central limit theorems.