  In this paper our aim is to characterize the set of extreme points of the set
of all n-dimensional copulas (n > 1). We have shown that a copula must induce a
singular measure with respect to Lebesgue measure in order to be an extreme
point in the set of n-dimensional copulas. We also have discovered some
sufficient conditions for a copula to be an extreme copula. We have presented a
construction of a small subset of n-dimensional extreme copulas such that any
n-dimensional copula is a limit point of that subset with respect to weak
convergence. The applications of such a theory are widespread, finding use in
many facets of current mathematical research, such as distribution theory,
survival analysis, reliability theory and optimization purposes. To illustrate
the point further, examples of how such extremal representations can help in
optimization have also been included.
