On families of bivariate copulas and their interrelation with the Hilbert space l2 and the Hilbert cube H

The Markov kernel based metric $D_1$ was introduced in 2011 in order to construct the scale-invariant dependence measure $ζ_1$, which assign each bivariate copula $C$ a dependence value in $[0,1]$, with $0$ exclusively for the case of independence, and $1$ exclusively for complete/functional depende