On a strong metric on the space of copulas and its induced dependence measure

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On the exact region determined by Kendall's τ and Spearman's ρ (2015, background): “A copula A ∈ C will be called completely dependent if and only if there exists h ∈ T such that K(x,E) := 1E(h(x)) is a Markov kernel of A (see [11, 19] for equivalent definitions and main properties).”
Conditioning-based metrics on the space of multivariate copulas and their interrelation with uniform and levelwise convergence and Iterated Function Systems (2015, methodology): “The following is a slight generalization of (non-mutual) complete dependence (on the first coordinate) to the multivariate setting (see [21,32]): Definition 1 A copula A ∈ Cρ is called completely dependent (w.”