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How to Prove Sklar’s Theorem

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Aggregation Functions in Theory and in Practise

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

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Abstract

In this contribution we stress the importance of Sklar’s theorem and present a proof of this result that is based on the compactness of the class of copulas (proved via elementary arguments) and the use of mollifiers. More details about the procedure can be read in a recent paper by the authors.

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Author information

Authors and Affiliations

  1. School of Economics and Management, Free University of Bozen-Bolzano, Bolzano, Italy

    Fabrizio Durante

  2. Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain

    Juan Fernández-Sánchez

  3. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce, Italy

    Carlo Sempi

Authors
  1. Fabrizio Durante
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  2. Juan Fernández-Sánchez
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  3. Carlo Sempi
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Corresponding author

Correspondence to Fabrizio Durante .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

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Durante, F., Fernández-Sánchez, J., Sempi, C. (2013). How to Prove Sklar’s Theorem. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_12

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  • DOI: https://doi.org/10.1007/978-3-642-39165-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

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