Sklar's Theorem

Let $H$ be a 2-D distribution function with marginal distribution functions $F$ and $G$. Then there exists a Copula $C$ such that

$$H(x,y)=C(F(x),G(y)).$$

Conversely, for any univariate distribution functions $F$ and $G$ and any Copula $C$, the function $H$ is a two-dimensional distribution function with marginals $F$ and $G$. Furthermore, if $F$ and $G$ are continuous, then $C$ is unique.