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Equivalence Between Limit Theorems for Lattice Group-Valued k-Triangular Set Functions

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Abstract

We investigate some of the main properties of lattice group-valued k-triangular set functions and we prove some Brooks–Jewett, Nikodým, Vitali–Hahn–Saks and Schur-type theorems and their equivalence. A Drewnowski-type theorem on existence of continuous restrictions of (s)-bounded set functions is given.

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Acknowledgements

(a) Our thanks to the anonymous referee for his/her remarks which improved the exposition of the paper.

(b) This research was partially supported by the Italian project “Ricerca di Base 2015, Teoria della Misura e dell’Approssimazione e applicazioni a svariati campi della matematica e alla ricostruzione di immagini”.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, via Vanvitelli, 1, 06123, Perugia, Italy

    Antonio Boccuto

  2. Department of Mathematics, University of Athens, Panepistimiopolis, 15784, Athens, Greece

    Xenofon Dimitriou

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  1. Antonio Boccuto
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  2. Xenofon Dimitriou
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Correspondence to Antonio Boccuto.

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Boccuto, A., Dimitriou, X. Equivalence Between Limit Theorems for Lattice Group-Valued k-Triangular Set Functions. Mediterr. J. Math. 15, 174 (2018). https://doi.org/10.1007/s00009-018-1222-9

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  • DOI: https://doi.org/10.1007/s00009-018-1222-9

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