Mediterranean Journal of Mathematics

, Volume 8, Issue 3, pp 431–450 | Cite as

Measure-Preserving Functions and the Independence Copula

  • Enrique de Amo
  • Manuel Díaz Carrillo
  • Juan Fernández-Sánchez


We solve a problem recently proposed by Kolesárová et al. Specifically, we prove that a necessary and sufficient condition for a given copula to be the independence or product copula is for the pair of measure-preserving transformations representing the copula to be independent as random variables.

We provide examples of such pairs for the well-known Cantor, Peano, and Hilbert curves. Moreover, a general constructive method is given for the representation of copulae in terms of measure-preserving transformations. In particular, we apply numbers representation systems to the study of self-similar copulae properties.

Mathematics Subject Classification (2010)

Primary 60E05 Secondary 28D05 


measure-preserving transformations independence or product copula representation system self-similarity 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Enrique de Amo
    • 1
  • Manuel Díaz Carrillo
    • 2
  • Juan Fernández-Sánchez
    • 1
  1. 1.Departamento de Álgebra y Análisis MatemáticoUniversidad de AlmeríaAlmeríaSpain
  2. 2.Departamento de Análisis MatemáticoUniversidad de GranadaGranadaSpain

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