Siburg, Karl FriedrichStoimenov, Pavel A.2007-10-252007-10-252007-10-25http://hdl.handle.net/2003/2479410.17877/DE290R-15316We introduce a scalar product for n-dimensional copulas, based on the Sobolev scalar product for W 1,2 -functions. The corresponding norm has quite remarkable properties and provides a new geometric framework for copulas. We show that, in the bivariate case, it measures invertibility properties with respect to the ∗-product for copulas defined by Darsow et al. The unique copula of minimal norm is the null element for the ∗-multiplication, whereas the copulas of maximal norm are precisely the invertible elements.enCopulaScalar productSobolev space004report