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Convergence Theorems in Interval-Valued Riemann–Lebesgue Integrability

Author

Listed:
  • Anca Croitoru

    (Faculty of Mathematics, University “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506 Jassy, Romania)

  • Alina Gavriluţ

    (Faculty of Mathematics, University “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506 Jassy, Romania)

  • Alina Iosif

    (Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploiesti, Bd. Bucureşti, No. 39, 100680 Ploiesti, Romania)

  • Anna Rita Sambucini

    (Department of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy)

Abstract

We provide some limit theorems for sequences of Riemann–Lebesgue integrable functions. More precisely, Lebesgue-type convergence and Fatou theorems are established. Then, these results are extended to the case of Riemann–Lebesgue integrable interval-valued multifunctions.

Suggested Citation

  • Anca Croitoru & Alina Gavriluţ & Alina Iosif & Anna Rita Sambucini, 2022. "Convergence Theorems in Interval-Valued Riemann–Lebesgue Integrability," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:450-:d:738801
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    Citations

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    Cited by:

    1. Anca Croitoru & Radko Mesiar & Anna Rita Sambucini & Bianca Satco, 2022. "Special Issue on Set Valued Analysis 2021," Mathematics, MDPI, vol. 10(15), pages 1-2, July.
    2. Leifan Yan & Tong Kang & Huai Zhang, 2023. "Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures," Mathematics, MDPI, vol. 11(13), pages 1-14, July.

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