  In this article, the concept of copulas is generalised to infinite
dimensional Hilbert spaces. We show one direction of Sklar's theorem and
explain that the other direction fails in infinite dimensional Hilbert spaces.
We derive a necessary and sufficient condition which allows to state this
direction of Sklar's theorem in Hilbert spaces. We consider copulas with
densities and specifically construct copulas in a Hilbert space by a family of
pairwise copulas with densities.
