Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (ℓ)-group-valued measures

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1. [1] Aviles Lopez A., Cascales Salinas B., Kadets V., Leonov A., The Schur l 1 theorem for filters, Zh. Mat. Fiz. Anal. Geom., 2007, 3(4), 383–398 Zbl1259.46017
2. [2] Barbieri G., Weber H., Measures on clans and on MV-algebras, In: Handbook on Measure Theory. II, North-Holland, Amsterdam, 2002, 911–945 http://dx.doi.org/10.1016/B978-044450263-6/50023-3 Zbl1019.28009
3. [3] Benvenuti P., Mesiar R., Vivona D., Monotone set functions-based integrals, In: Handbook on Measure Theory. II, North-Holland, Amsterdam, 2002, 1329–1379 http://dx.doi.org/10.1016/B978-044450263-6/50034-8 Zbl1099.28007
4. [4] Bernau S.J., Unique representation of Archimedean lattice group and normal Archimedean lattice rings, Proc. London Math. Soc., 1965, 15, 599–631 http://dx.doi.org/10.1112/plms/s3-15.1.599 Zbl0134.10802
5. [5] Boccuto A., Vitali-Hahn-Saks and Nikodym theorems for means with values in Riesz spaces, Atti Sem. Mat. Fis. Univ. Modena, 1996, 44(1), 157–173 Zbl0864.28003
6. [6] Boccuto A., Dieudonné-type theorems for means with values in Riesz spaces, Tatra Mt. Math. Publ., 1996, 8, 29–42 Zbl0918.28009
7. [7] Boccuto A., Egorov property and weak σ-distributivity in Riesz spaces, Acta Mathematica (Nitra), 2003, 6, 61–66 
8. [8] Boccuto A., Candeloro D., Dieudonné-type theorems for set functions with values in (l)-groups, Real Anal. Exchange, 2001/2002, 27(2), 473–484 Zbl1067.28011
9. [9] Boccuto A., Candeloro D., Some new results about Brooks-Jewett and Dieudonné-type theorems in (L)-groups, Kybernetika (Prague), 2010, 46(6), 1049–1060 Zbl1210.28015
10. [10] Boccuto A., Candeloro D., Uniform (s)-boundedness and regularity for (l)-group-valued measures, Cent. Eur. J. Math., 2011, 9(2), 433–440 http://dx.doi.org/10.2478/s11533-010-0097-1 Zbl1217.28020
11. [11] Boccuto A., Dimitriou X., Papanastassiou N., Basic matrix theorems for I-convergence in (l)-groups, Math. Slovaca, 2011 (in press) Zbl1313.28021
12. [12] Boccuto A., Dimitriou X., Papanastassiou N., Brooks-Jewett-type theorems for the pointwise ideal convergence of measures with values in (l)-groups, Tatra Mt. Math. Publ., 2011 (in press) Zbl1265.26035
13. [13] Boccuto A., Dimitriou X., Papanastassiou N., Schur lemma and limit theorems in (l)-groups with respect to filters, Math. Slovaca, 2011 (in press) Zbl1274.28027
14. [14] Boccuto A., Riečan B., Vrábelová M., Kurzweil-Henstock Integral in Riesz Spaces, Bentham Science Publishers, 2009 
15. [15] Brooks J.K., On a theorem of Dieudonné, Adv. Math., 1980, 36(2), 165–168 http://dx.doi.org/10.1016/0001-8708(80)90014-6 
16. [16] Candeloro D., Sui teoremi di Vitali-Hahn-Saks, Dieudonné e Nikodým, Rend. Circ. Mat. Palermo Suppl., 1985, 8, 439–445 
17. [17] Candeloro D., Letta G., Sui teoremi di Vitali-Hahn-Saks e di Dieudonné, Rend. Accad. Naz. Sci. XL Mem. Mat., 1985, 9(1), 203–213 
18. [18] Dieudonné J., Sur la convergence des suites de mesures de Radon, An. Acad. Brasil. Ciênc., 1951, 23, 21–38, 277–282 Zbl0043.11202
19. [19] Dvurečenskij A., Measures on quantum structures, In: Handbook on Measure Theory. II, North-Holland, Amsterdam, 2002, 827–868 http://dx.doi.org/10.1016/B978-044450263-6/50021-X Zbl1031.28003
20. [20] de Lucia P., Pap E., Convergence theorems for set functions, In: Handbook on Measure Theory. I, North-Holland, Amsterdam, 2002, 125–178 Zbl1034.28002
21. [21] Pap E., Pseudo-additive measures and their applications, In: Handbook on Measure Theory. II, North-Holland, Amsterdam, 2002, 1403–1468 http://dx.doi.org/10.1016/B978-044450263-6/50036-1 Zbl1018.28010
22. [22] Riečan B., Mundici D., Probability on MV-algebras, In: Handbook on Measure Theory. I, North-Holland, Amsterdam, 2002, 869–909 Zbl1017.28002

1. Antonio Boccuto, Xenofon Dimitriou, Dieudonné-type theorems for lattice group-valued $k$-triangular set functions