Uniform (s)-boundedness and regularity for (l)-group-valued measures

• Autorzy: Antonio Boccuto , Domenico Candeloro
• Języki publikacji: EN

Abstrakty

EN

Some new results about uniform (s)-boundedness for regular (l)-group-valued set functions are given.

Słowa kluczowe

EN

(l)-group; Order convergence; Brooks-Jewett theorem; Regular set function; Uniform (s)-boundedness

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 2
• Strony: 433-440

Daty

wydano

2011-04-01

online

2011-02-18

Twórcy

autor

Antonio Boccuto

• University of Perugia,

autor

Domenico Candeloro

• University of Perugia,

Bibliografia

• [1] Barbieri G., On the Dieudonné theorem, Sci. Math. Jpn., 2009, 70(3), 279–284
• [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
• [3] Boccuto A., Dieudonné-type theorems for means with values in Riesz spaces, Tatra Mt. Math. Publ., 1996, 8, 29–42
• [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
• [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)
• [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
• [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
• [13] Dieudonné J., Sur la convergence des suites de mesures de Radon, An. Acad. Brasil. Ciênc., 1951, 23, 21–38, 277–282
• [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
• [16] Vulikh B.Z., Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff, Groningen, 1967
• [17] Wright J.D.M., The measure extension problem for vector lattices, Ann. Inst. Fourier (Grenoble), 1971, 21(4), 65–85

Identyfikatory

DOI

10.2478/s11533-010-0097-1