On mappings preserving measurability

Authors:
JóZsef Bukor;Ladislav MišíK;JáNos T. TóTh
Affiliations:
Department of Mathematics and Informatics, J. Selye University in Komárno, Komárno, Slovak Republic;Department of Mathematics, University of Ostrava & Centre of Excellence IT4Innovations - Division UO - IRAFM, 30. dubna 22, 701 03 Ostrava 1, Czech Republic;Department of Mathematics and Informatics, J. Selye University in Komárno, Komárno, Slovak Republic
Venue:
Information Sciences: an International Journal
Year:
2013

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Abstract

Let @m=(@m"n) be a universal fuzzy measure and let M(@m) be the set of all @m-measurable sets, i.e. sets A@?N for which the limit @m^*(A)=lim"n"-"~@m"n(A@?{1,2,...,n}) exists. We are studying properties of measurability preserving injective mappings, i.e. injective mappings @p:N-N such that A@?M(@m) implies @p(A)@?M(@m). Under some assumptions on @m we prove @m^*(@p(A))=@l@m^*(A) for all A@?M(@m), where @l=@m^*(@p(N)).