Copulae of probability measures on product spaces
The author generalizes the construction of copulas given by \textit{M. Sklar} [Publ. Inst. Statist. Univ. Paris 8, 229-231 (1960; Zbl 0100.142)] to probability measures on Polish product spaces. This gives a representation of the form \[ \mu (A_ 1\times...\times A_ n)=C(P_ 1(A_ 1),...,P_ n(A_ n)) \] for a probability measure \(\mu\) with marginals \(P_ 1,...,P_ n\). As an application \textit{G. Dall'Aglio}'s [see ``Probability theory.'' (1987; Zbl 0609.60001)] characterization of the convergence in probability is generalized. Reviewer's remark: A result closely related to the main result of this paper has been proved independently in a paper by Rachev and R schendorf, to be published in Theory Probab. Appl. (1990).
characterization of the convergence in probability
scientific article; zbMATH DE number 4145025
scientific article