Copulas: Grounded or increasing functions.

Question

For a function $H(x,y)$ to be a copula, it has to be increasing in $x$ and in $y$. But, instead of this condition, other authors say that the function has to be grounded. Are these properties equivalent?. I cannot prove that if $H(x,y)$ is increasing in $x$ and $y$, then it is grounded. Any help will be appreciated.

Answer 1

If $H(x, y)= x + y -1$ we have a function that fulfills our three properties or requirements, but it is not grounded.