Abstract
Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.
[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 Search in Google Scholar
[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/B978-044450263-6/50023-310.1016/B978-044450263-6/50023-3Search in Google Scholar
[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/B978-044450263-6/50034-810.1016/B978-044450263-6/50034-8Search in Google Scholar
[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/s3-15.1.59910.1112/plms/s3-15.1.599Search in Google Scholar
[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 Search in Google Scholar
[6] Boccuto A., Dieudonné-type theorems for means with values in Riesz spaces, Tatra Mt. Math. Publ., 1996, 8, 29–42 Search in Google Scholar
[7] Boccuto A., Egorov property and weak σ-distributivity in Riesz spaces, Acta Mathematica (Nitra), 2003, 6, 61–66 Search in Google Scholar
[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 10.14321/realanalexch.27.2.0473Search in Google Scholar
[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 Search in Google Scholar
[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/s11533-010-0097-110.2478/s11533-010-0097-1Search in Google Scholar
[11] Boccuto A., Dimitriou X., Papanastassiou N., Basic matrix theorems for I-convergence in (l)-groups, Math. Slovaca, 2011 (in press) 10.2478/s12175-012-0053-6Search in Google Scholar
[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) 10.2478/v10127-011-0021-5Search in Google Scholar
[13] Boccuto A., Dimitriou X., Papanastassiou N., Schur lemma and limit theorems in (l)-groups with respect to filters, Math. Slovaca, 2011 (in press) 10.2478/s12175-012-0070-5Search in Google Scholar
[14] Boccuto A., Riečan B., Vrábelová M., Kurzweil-Henstock Integral in Riesz Spaces, Bentham Science Publishers, 2009 Search in Google Scholar
[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)90014-610.1016/0001-8708(80)90014-6Search in Google Scholar
[16] Candeloro D., Sui teoremi di Vitali-Hahn-Saks, Dieudonné e Nikodým, Rend. Circ. Mat. Palermo Suppl., 1985, 8, 439–445 Search in Google Scholar
[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 Search in Google Scholar
[18] Dieudonné J., Sur la convergence des suites de mesures de Radon, An. Acad. Brasil. Ciênc., 1951, 23, 21–38, 277–282 Search in Google Scholar
[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-X10.1016/B978-044450263-6/50021-XSearch in Google Scholar
[20] de Lucia P., Pap E., Convergence theorems for set functions, In: Handbook on Measure Theory. I, North-Holland, Amsterdam, 2002, 125–178 10.1016/B978-044450263-6/50005-1Search in Google Scholar
[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/B978-044450263-6/50036-110.1016/B978-044450263-6/50036-1Search in Google Scholar
[22] Riečan B., Mundici D., Probability on MV-algebras, In: Handbook on Measure Theory. I, North-Holland, Amsterdam, 2002, 869–909 10.1016/B978-044450263-6/50022-1Search in Google Scholar
© 2011 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
