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Keywords = setwise convergence

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16 pages, 324 KB  
Article
Vitali Theorems for Varying Measures
by Valeria Marraffa and Anna Rita Sambucini
Symmetry 2024, 16(8), 972; https://doi.org/10.3390/sym16080972 - 31 Jul 2024
Cited by 2 | Viewed by 2188
Abstract
The classical Vitali theorem states that, under suitable assumptions, the limit of a sequence of integrals is equal to the integral of the limit functions. Here, we consider a Vitali-type theorem of the following form [...] Read more.
The classical Vitali theorem states that, under suitable assumptions, the limit of a sequence of integrals is equal to the integral of the limit functions. Here, we consider a Vitali-type theorem of the following form fndmnfdm for a sequence of pair (fn,mn)n and we study its asymptotic properties. The results are presented for scalar, vector and multivalued sequences of mn-integrable functions fn. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense for Pettis and McShane integrability. A list of known results on this topic is cited and new results are obtained when the ambient space Ω is not compact. Full article
(This article belongs to the Section Mathematics)
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