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

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1. [1] Barbieri G., On the Dieudonné theorem, Sci. Math. Jpn., 2009, 70(3), 279–284 Zbl1188.28015
2. [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 Zbl0134.10802
3. [3] Boccuto A., Dieudonné-type theorems for means with values in Riesz spaces, Tatra Mt. Math. Publ., 1996, 8, 29–42 Zbl0918.28009
4. [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 Zbl1067.28011
5. [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. [6] Boccuto A., Candeloro D., Some new results about Brooks-Jewett and Dieudonné-type theorems in (Z)-groups, Kybernetika (Prague), 2010 (in press) Zbl1210.28015
7. [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. [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. [9] Candeloro D., Sui teoremi di Vitali-Hahn-Saks, Dieudonné e Nikodým, Rend. Circ. Mat. Palermo Suppl., 1985, 8, 439–445 
10. [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. [11] De Lucia P., Pap E., Convergence theorems for set functions, In: Handbook on Measure Theory, vol. I, North-Holland, Amsterdam, 2002, 125–178 Zbl1034.28002
12. [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 Zbl1152.28015
13. [13] Dieudonné J., Sur la convergence des suites de mesures de Radon, An. Acad. Brasil. Ciênc., 1951, 23, 21–38, 277–282 Zbl0043.11202
14. [14] Luxemburg W.A.J., Zaanan A.C., Riesz Spaces I, North-Holland Mathematical Library, North-Holland, Amsterdam-London, 1971 
15. [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 Zbl1195.28004
16. [16] Vulikh B.Z., Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff, Groningen, 1967 Zbl0186.44601
17. [17] Wright J.D.M., The measure extension problem for vector lattices, Ann. Inst. Fourier (Grenoble), 1971, 21(4), 65–85 Zbl0215.48101

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