Ararat, ÇağınHamel, A. H.2021-03-042021-03-0420200040-585Xhttp://hdl.handle.net/11693/75742It is shown that a recently introduced lower cone distribution function, together with the set-valued multivariate quantile, generates a Galois connection between a complete lattice of closed convex sets and the interval [0, 1]. This generalizes the corresponding univariate result. It is also shown that an extension of the lower cone distribution function and the set-valued quantile characterize the capacity functional of a random set extension of the original multivariate variable along with its distribution.EnglishGalois connectionMultivariate quantileComplete latticeLower cone distribution functionRandom setLower cone distribution functions and set-valued quantiles form galois connectionsArticle10.1137/S0040585X97T989908