Shuffles of Min.
Stochastica, Tome 13 (1992) no. 1, p. 61.

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Copulas are functions which join the margins to produce a joint distribution function. A special class of copulas called shuffles of Min is shown to be dense in the collection of all copulas. Each shuffle of Min is interpreted probabilistically. Using the above-mentioned results, it is proved that the joint distribution of any two continuously distributed random variables X and Y can be approximated uniformly, arbitrarily closely by the joint distribution of another pair X* and Y* each of which is almost surely an invertible function of the other such that X and X* are identically distributed as are Y and Y*. The preceding results shed light on A. Rényi's axioms for a measure of dependence and a modification of those axioms as given by B. Schweizer and E.F. Wolff.
Classification : 62H05, 62H20, 62E10, 60B10
Mots-clés : Función cópula, Dependencia estocástica, Teoría de la distribución, Distribución marginal, doubly stochastic measure, functional dependence, stochastic independence, copulas, measure of dependence 
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     author = {Piotr Mikusinski and Howard Sherwood and Michael D. Taylor},
     title = {Shuffles of {Min.}},
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Piotr Mikusinski; Howard Sherwood; Michael D. Taylor. Shuffles of Min.. Stochastica, Tome 13 (1992) no. 1, p. 61. https://geodesic-test.mathdoc.fr/item/STO_1992__13_1_39282/