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A measure, μ, on (0,1) 2 is said to be D 4 -invariant if its value for any Borel set is invariant with respect to the symmetries of the unit square. A function, K, generated in a certain way by a measure, μ, on (0,1) 2 is shown to be a measure of concordance if and only if the generating measure is positive, regular, D 4 -invariant, and satisfies certain inequalities. The construction examined here includes Blomqvist's beta as a special case.

Measures of concordance determined by 𝐷₄-invariant measures on (0,1)²