A Topological Proof of Sklar's Theorem in Arbitrary Dimensions

TL;DR

This paper provides a topological proof of Sklar's theorem applicable in infinite-dimensional spaces, expanding the theorem's theoretical foundation using inverse systems.

Contribution

It introduces a novel topological approach to prove Sklar's theorem in arbitrary dimensions, which was previously unestablished.

Findings

Sklar's theorem holds in infinite-dimensional spaces.

Topological methods can be used to prove fundamental probabilistic theorems.

The approach generalizes the theorem beyond finite dimensions.

Abstract

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.