Author: "Tóth, János T." / Topic: asymptotic density - Searchworks@Jio Institute Digital Library Search Results

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Start Over Author "Tóth, János T." Topic asymptotic density

Author: Grekos, Georges, Mišík, Ladislav, and Tóth, János T.
Subjects: *SET theory, *ASYMPTOTIC expansions, *NUMBER theory, *DARBOUX transformations, *CONVEX sets, *MATHEMATICAL analysis
Abstract: Abstract: Extending previous results, we give a new description of the density set, that is the set of all pairs of densities – upper and lower – of all subsets of a given set of positive integers. The extension consists in using the concept of weighted density with the weight function satisfying two standard conditions. In order to prove that the density set is convex, we establish and use the joint Darboux property of the weighted density. Finally we prove that the density set is closed through an explicit characterization of its upper boundary. [Copyright &y& Elsevier]
Published: 2010
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Author: Bukor, József, Mišík, Ladislav, and Tóth, János T.
Subjects: *MATHEMATICAL mappings, *FUZZY measure theory, *SET theory, *INJECTIVE functions, *MATHEMATICAL analysis, *CONTINUOUS functions
Abstract: Abstract: Let μ =(μ n ) be a universal fuzzy measure and let be the set of all μ-measurable sets, i.e. sets for which the limit μ ∗(A)=lim n→∞ μ n (A ∩{1,2,…, n}) exists. We are studying properties of measurability preserving injective mappings, i.e. injective mappings such that implies . Under some assumptions on μ we prove μ ∗(π(A))= λμ ∗(A) for all , where . [Copyright &y& Elsevier]
Published: 2013
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