A copula is a function which joins (or 'couples') a bivariate distribution function to its marginal (one-dimensional) distribution functions. In this paper, we obtain Chebyshev type inequalities by utilising copulas.

Let P be a compact n-dimensional convex polyhedron in R n containing the origin in its interior and let e H(t) = Z 1 0 Z vP e 2it ddv, t2 R n ;where vP is the characteristic function of the dilated polyhedron vP. Let H N (t) = X m2Z n e H 1 N+1 (t+m), t 2 T n , where e H " (t) = " ?n e H(t="). We prove that (e H " f)(t) ! f(t) a.e., as " ! 0, for any f 2 L 1 (R n), and that (H N f)(t) ! f(t) a....

Matloob Anwar,1 Naveed Latif,1 and J. Pečarić1, 2 1 Abdus Salam School of Mathematical Sciences, 68-B New Muslim Town, GC University, Lahore 54000, Pakistan 2 Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, Zagreb 10000, Croatia Correspondence should be addressed to Naveed Latif, [email protected] Received 9 October 2008; Accepted 2 February 2009 Recommended by Wing-S...

For a family $$(\mathscr {A}_x)_{x \in (0,1)}$$ of integral quasi-arithmetic means satisfying certain measurability-type assumptions we search for an mean K such that $$K\big ((\mathscr {A}_x(\mathbb {P}))_{x (0,1)}\big )=K(\mathbb {P})$$ every compactly supported probability Borel measure $$\mathbb {P}$$ . Also some results concerning the uniqueness invariant will be given.