Convergence for varying measures

Some limit theorems of the type∫Ωfndmn→∫Ωfdm are presented for scalar, (vector), (multi)-valued sequences of mn-integrable functions fn. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2023-02, Vol.518 (2), p.126782, Article 126782
Main Authors: Di Piazza, L., Marraffa, V., Musiał, K., Sambucini, A.R.
Format: Article
Language:English
Subjects:
Absolute integrability
Convergence in total variation
Multifunction
Pettis integral
Setwise convergence
Uniform integrability
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Summary:Some limit theorems of the type∫Ωfndmn→∫Ωfdm are presented for scalar, (vector), (multi)-valued sequences of mn-integrable functions fn. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126782