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

  • Antonio BoccutoEmail author
  • Xenofon Dimitriou


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.


Lattice group k-triangular set function continuous set function (s)-bounded set function Fremlin lemma limit theorem 

Mathematics Subject Classification

26E50 28A12 28A33 28B10 28B15 40A35 46G10 



(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. 1.Dipartimento di Matematica e InformaticaUniversita degli Studi di PerugiaPerugiaItaly
  2. 2.Department of MathematicsUniversity of AthensAthensGreece

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