On mappings preserving measurability
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)....
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Published in | Information sciences Vol. 235; pp. 323 - 328 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
20.06.2013
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Subjects | |
Online Access | Get full text |
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Summary: | 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)). |
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ISSN: | 0020-0255 1872-6291 |
DOI: | 10.1016/j.ins.2013.02.007 |