Uniform (s)-boundedness and regularity for (l)-group-valued measures
Antonio Boccuto ; Domenico Candeloro
Open Mathematics, Tome 9 (2011), p. 433-440 / Harvested from The Polish Digital Mathematics Library
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Some new results about uniform (s)-boundedness for regular (l)-group-valued set functions are given.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:268941 
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     author = {Antonio Boccuto and Domenico Candeloro},
     title = {Uniform (s)-boundedness and regularity for (l)-group-valued measures},
     journal = {Open Mathematics},
     volume = {9},
     year = {2011},
     pages = {433-440},
     zbl = {1217.28020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0097-1}
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Antonio Boccuto; Domenico Candeloro. Uniform (s)-boundedness and regularity for (l)-group-valued measures. Open Mathematics, Tome 9 (2011) pp. 433-440. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0097-1/

[1] Barbieri G., On the Dieudonné theorem, Sci. Math. Jpn., 2009, 70(3), 279–284 | Zbl 1188.28015

[2] Bernau S.J., Unique representation of Archimedean lattice groups and normal Archimedean lattice rings, Proc. London Math. Soc, 1965, 15, 599–631 http://dx.doi.org/10.1112/plms/s3-15.1.599 | Zbl 0134.10802

[3] Boccuto A., Dieudonné-type theorems for means with values in Riesz spaces, Tatra Mt. Math. Publ., 1996, 8, 29–42 | Zbl 0918.28009

[4] Boccuto A., Candeloro D., Dieudonné-type theorems for set functions with values in (Z)-groups, Real Anal. Exchange, 2001/02, 27(2), 473–484 | Zbl 1067.28011

[5] Boccuto A., Candeloro D., Uniform s-boundedness and convergence results for measures with values in complete l-groups, J. Math. Anal. Appl., 2002, 265(1), 170–194 http://dx.doi.org/10.1006/jmaa.2001.7715

[6] Boccuto A., Candeloro D., Some new results about Brooks-Jewett and Dieudonné-type theorems in (Z)-groups, Kybernetika (Prague), 2010 (in press) | Zbl 1210.28015

[7] Brooks J.K., On a theorem of Dieudonné, Adv. in Math., 1980, 36(2), 165–168 http://dx.doi.org/10.1016/0001-8708(80)90014-6

[8] Brooks J.K., Chacon R.V., Continuity and compactness of measures, Adv. in Math., 1980, 37(1), 16–26 http://dx.doi.org/10.1016/0001-8708(80)90023-7

[9] Candeloro D., Sui teoremi di Vitali-Hahn-Saks, Dieudonné e Nikodým, Rend. Circ. Mat. Palermo Suppl., 1985, 8, 439–445

[10] 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

[11] De Lucia P., Pap E., Convergence theorems for set functions, In: Handbook on Measure Theory, vol. I, North-Holland, Amsterdam, 2002, 125–178 | Zbl 1034.28002

[12] De Lucia P., Pap E., Cafiero approach to Dieudonné type theorems, J. Math. Anal. Appl., 2008, 337(2), 1151–1157 http://dx.doi.org/10.1016/j.jmaa.2007.03.113 | Zbl 1152.28015

[13] Dieudonné J., Sur la convergence des suites de mesures de Radon, An. Acad. Brasil. Ciênc., 1951, 23, 21–38, 277–282 | Zbl 0043.11202

[14] Luxemburg W.A.J., Zaanan A.C., Riesz Spaces I, North-Holland Mathematical Library, North-Holland, Amsterdam-London, 1971

[15] Ventriglia F., Dieudonnés theorem for non-additive set functions, J. Math. Anal. Appl., 2010, 367(1), 296–303 http://dx.doi.org/10.1016/j.jmaa.2010.01.017 | Zbl 1195.28004

[16] Vulikh B.Z., Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff, Groningen, 1967 | Zbl 0186.44601

[17] Wright J.D.M., The measure extension problem for vector lattices, Ann. Inst. Fourier (Grenoble), 1971, 21(4), 65–85 | Zbl 0215.48101