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Upper and lower limits of sequences of measurable sets and of sets with the Baire property. (English) Zbl 1122.28003

Summary: The note presents the study of the behaviour of upper and lower limits of a sequence \(\{A_n\}_{n\in N}\) of \(S\)-measurable subsets of the unit interval \([0,1]\) when all sets \(A_n\) are subject to small translations. \(S\) is here the class of all Lebesgue measurable sets or the class of sets with the Baire property. The last two theorems describe a new (density point) approach to the convergence of Rademacher’s type sequences of sets and functions and generalise the result of K. P. Rath [Real Anal. Exch. 21, No. 1, 304–307 (1996; Zbl 0846.28003)].

MSC:

28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
28A99 Classical measure theory
54A99 Generalities in topology

Citations:

Zbl 0846.28003
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