A Detailed and Direct Proof of Skorohod-Wichura's Theorem

The representation Skorohod theorem of weak convergence of random variables on a metric space
goes back to Skorohod (1956) in the case where the metric space is the class of real-valued functions
defined on [0,1] which are right-continuous and have left-hand limits when endowed with the
Skorohod metric. Among the extensions of that to metric spaces, the version by Wichura (1970)
seems to be the most fundamental. But the proof of Wichura seems to be destined to a very
restricted public. We propose a more detailed proof to make it more accessible at the graduate
level. However we do far more by simplifying it since important steps in the original proof are
dropped, which leads to a direct proof that we hope to be more understandable to a larger spectrum
of readers. The current version is more appropriate for different kinds of generalizations.