## 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.

**Author (s) Details**

**Gane Samb Lo**

LERSTAD, Gaston Berger University, Saint-Louis, Senegal and LSTA, Pierre and Marie Curie University, Paris VI, France and AUST – African University of Science and Technology, Abuja, Nigeria.

**View Book :- **https://bp.bookpi.org/index.php/bpi/catalog/book/237

arbitrary products complete spaces. product spaces Skorohod-Wichura theorem weak convergence of probability measure