A note on quasi-copulas and signed measures

In this note we provide two alternative proofs to that given in Nelsen et al. [Quasi-copulas and signed measures, Fuzzy Sets Syst. 161 (2010) 2328–2336] of the fact that the best possible lower bound for the set of n-quasi-copulas does not induce a stochastic measure on [ 0 , 1 ] n for n ⩾ 3 : firstly, by focusing on its mass distribution, and secondly, by using concepts of self-affinity.