Editorial to the special issue on "Random Variables, Joint Distribution Functions, and Copulas"

= 0 if x j = 0 for at least one index j, and (3) all n-dimensional differences of C are nonnegative. There he further announced what we now call Sklar's theorem. In the Kybernetika paper he sketched the proof of the above statement, developed some of its consequences, and discussed various connections between copulas and random variables, associative copulas, binary operations on spaces of one-dimensional distribution functions induced by copulas, and applications to probabilistic metric spaces and probabilistic information spaces. At the time copulas were used almost exclusively in the theory of Probabilistic Metric Spaces [15]. Only some years later, after the publication of the paper by Schweizer and Wolff [16], did the statistical community " discover " copulas. This had two effects: on the one hand, it was quickly realized that copulas were of paramount importance in dealing with questions concerning the dependence of random variables, and, on the other hand the number of papers dealing with copulas, under both the theoretical and the applied aspects, grew enormously. For a brief history of the early years of copula theory we refer the reader to Schweizer's synthesis [14]. After nearly 50 years from their introduction, copulas can be considered as a standard tool for the constructions of stochastic models, as clearly stated in the books by Joe [9] and Nelsen [12]. As a consequence, they are frequently used in finance: see, just to make few examples, the books by Cherubini et al. [3] and Mc Neil et al. [11], and the recent survey papers by Embrechts [4] and Genest et al. [6]. Moreover, copulas were also found to be of great interest in environmental sciences, especially hydrology: see the book by Salvadori et al. [13] and the paper by Genest and Favre [5]. Outside the field of applied probability and statistics, they appear, for example, in the theory of functional equations and inequalities [1] and fuzzy set