{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T12:49:18Z","timestamp":1765889358021,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research project of MIUR (Italian Ministry of Education, University and Research) Prin 2022 \u201cNonlinear differential problems with applications to real phenomena\u201d","award":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"],"award-info":[{"award-number":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"]}]},{"name":"PRIN 2022 PNRR: \u201cRETINA: REmote sensing daTa INversion with multivariate functional modelling for essential climAte variables characterization\u201d funded by the European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU","award":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"],"award-info":[{"award-number":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"]}]},{"name":"Gnampa Project 2024 \u201cDynamical Methods: Inverse problems, Chaos and Evolution\u201d","award":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"],"award-info":[{"award-number":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"]}]},{"name":"F.F.R. 2024: University of Palermo","award":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"],"award-info":[{"award-number":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"]}]},{"name":"Ricerca di Base, Universit\u00e0 degli Studi di Perugia","award":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"],"award-info":[{"award-number":["2022ZXZTN2","CUP J53D23003920006","P20229SH29","CUP: J53D23015950001)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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 \u222bfndmn\u2192\u222bfdm 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 \u03a9 is not compact.<\/jats:p>","DOI":"10.3390\/sym16080972","type":"journal-article","created":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T15:26:53Z","timestamp":1722526013000},"page":"972","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Vitali Theorems for Varying Measures"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1439-5501","authenticated-orcid":false,"given":"Valeria","family":"Marraffa","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Sciences, University of Palermo, 34, Via Archirafi, 90123 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0161-8729","authenticated-orcid":false,"given":"Anna Rita","family":"Sambucini","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF03013514","article-title":"Sull\u2019integrazione per serie","volume":"23","author":"Vitali","year":"1907","journal-title":"Rend. 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