  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.
