A convex combination of k joint CDFs is itself a joint CDF (finite mixture), but is a convex combination of k copula functions a copula function itself?  Suppose Y = (Y1,...,Yd) has a meta-Gaussian...

A convex combination of k joint CDFs is itself a joint CDF (finite mixture), but is a convex combination of k copula functions a copula function itself?

 Suppose Y = (Y1,...,Yd) has a meta-Gaussian distribution with continuous marginal distributions and copula CGauss(·|Ω). Show that if ρτ (Yi, Yj ) = 0 then Yi and Yj are independent.