| Abstract: |
| Some limit theorems of the type
$$\int_{\Omega}f_n\,dm_n \rightarrow \int_{\Omega}f \,dm$$
are presented for scalar, (vector), (multi)-valued sequences of $m_n$-integrable functions $f_n$.
Conditions for the convergence of sequences of measures $(m_n)_n$ and of their integrals $(\int f_n dm_n)_n$ in a measurable space $\Omega $ are of interest in many areas of pure and applied mathematics such as statistics, transportation problems, interactive partial systems,
neural networks and signal processing.
Sufficient conditions in order to obtain some kind of Vitali`s convergence theorems for a sequence of
(multi)functions $(f_n)_n$ integrable with respect to a sequence of measures $(m_n)_n$ are considered.
We consider the asymptotic properties of $(\int_{\Omega} f_n d m_n)_n$ with respect to varying measures, which are vaguely convergent in an arbitrary measurable spaces.
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Convergence for varying measures, J. Math. Anal. Appl.,
Vol. 518, N.2, Paper N. 126782, (2023).
\bibitem{3} L. Di Piazza, V. Marraffa, K. Musia{\l}, A. Sambucini,
Convergence for varying measures in the topological case, Annali di Matematica Pura e Applicata, (4) 203 (2024) 71-86.
\bibitem{2}V. Marraffa, B. Satco,
Convergence Theorems for Varying Measures Under Convexity Conditions and Applications,
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\bibitem{4} V. Marraffa, A.R. Sambucini, Vitali theorems for varying measure, Symmetry 2024, 16(8), 972.
\end{thebibliography} |
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