On mappings preserving measurability

• Published in: Information sciences Vol. 235; pp. 323 - 328
• Main Authors: Bukor, József, Mišík, Ladislav, Tóth, János T.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 20.06.2013
• Subjects: Asymptotic density; Asymptotic fuzzy measure; Universal fuzzy measure; Universal fuzzy measure; Asymptotic fuzzy measure; Asymptotic density
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2013.02.007

Let μ=(μn) be a universal fuzzy measure and let M(μ) be the set of all μ-measurable sets, i.e. sets A⊂N for which the limit μ∗(A)=limn→∞μn(A∩{1,2,…,n}) exists. We are studying properties of measurability preserving injective mappings, i.e. injective mappings π:N→N such that A∈M(μ) implies π(A)∈M(μ). Under some assumptions on μ we prove μ∗(π(A))=λμ∗(A) for all A∈M(μ), where λ=μ∗(π(N)).