Siburg, Karl F.Stoimenov, Pavel A.2008-05-152008-05-152008-05-15http://hdl.handle.net/2003/2527010.17877/DE290R-8063We 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 of copulas with respect to the *-operation introduced by Darsow et al. (1992). The unique copula of minimal norm is the null element for the *-operation, whereas the copulas of maximal norm are precisely the invertible elements.enPreprints der Fakultät für Mathematik;2008-07CopulaScalar productSobolev space510preprint