A characterization of quasi-copulas (Q1293663)

A function \(Q:[0,1]^2\to[0,1]\) is a quasi-copula if and only if it satisfies the three following conditions: (i) \(Q(0,x)=Q(x,0)=0\), \(Q(x,1)=Q(1,x)=x\), \(x\in[0,1]\); (ii) \(Q(x,y)\) is non-decreasing in each of its arguments; (iii) \(Q\) satisfies a Lipschitz condition. The quasi-copula is comprised between the Fréchet bounds. The distinction between copulas and proper quasi-copulas is studied. Absolutely continuous quasi-copulas are not necessarily copulas.