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<p>In this paper, we investigate several subsets of <i>n</i>-copulas and <i>n</i>-quasi-copulas from the perspective of convex lineability and the recently introduced concept of convex spaceability. Our purpose is to determine when such families contain extremely large algebraic structures, namely linearly independent sets of cardinality of the continuum whose convex hull, and in some cases a closed convex linearly independent subset, remain entirely inside the class under study. These include the families of asymmetric copulas, copulas with maximal asymmetric measure, and proper <i>n</i>-quasi-copulas, among others. In contrast, for several other natural classes of copulas, we show that (maximal) convex lineability holds, while convex spaceability remains an open problem.</p>

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Convex Lineability in Copula and Quasi-copula Sets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月21日

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  • Enrique de Amo,
  • Juan Fernández-Sánchez,
  • David García-Fernández,
  • Manuel Úbeda-Flores

摘要

In this paper, we investigate several subsets of n-copulas and n-quasi-copulas from the perspective of convex lineability and the recently introduced concept of convex spaceability. Our purpose is to determine when such families contain extremely large algebraic structures, namely linearly independent sets of cardinality of the continuum whose convex hull, and in some cases a closed convex linearly independent subset, remain entirely inside the class under study. These include the families of asymmetric copulas, copulas with maximal asymmetric measure, and proper n-quasi-copulas, among others. In contrast, for several other natural classes of copulas, we show that (maximal) convex lineability holds, while convex spaceability remains an open problem.