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Brooks-Jewett-type theorems for the pointwise ideal convergence of measures with values in (l)-groups


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[1] BALCERZAK, M.-DEMS, K.-KOMISARSKI, A.: Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007), 715-729.10.1016/j.jmaa.2006.05.040Search in Google Scholar

[2] BERNAU, S. J.: Unique representation of Archimedean lattice group and normal Archimedean lattice rings, Proc. London Math. Soc. 15 (1965), 599-631.10.1112/plms/s3-15.1.599Search in Google Scholar

[3] BOCCUTO, A.: Vitali-Hahn-Saks and Nikodym theorems for means with values in Riesz spaces, Atti Sem. Mat. Fis. Univ. Modena 44 (1996), 157-173.Search in Google Scholar

[4] BOCCUTO, A.: Egorov property and weak _-distributivity in Riesz spaces, Acta Math. (Nitra) 6 (2003), 61-66.Search in Google Scholar

[5] BOCCUTO, A.-CANDELORO, D.: Uniform s-boundedness and convergence results for measures with values in complete l-groups, J. Math. Anal. Appl. 265 (2002), 170-194.10.1006/jmaa.2001.7715Search in Google Scholar

[6] BOCCUTO, A.-CANDELORO, D.: Defining limits by means of integrals, Oper. Theory Adv. Appl. 201 (2009), 79-87.Search in Google Scholar

[7] BOCCUTO, A.-DIMITRIOU, X.-PAPANASTASSIOU, N.: Limit theorems in (l)- -groups with respect to (D)-convergence, Dipartimento di Matematica e Informatica, Uni- versity of Perugia, Technical Report n. 2010/5.Search in Google Scholar

[8] BOCCUTO, A.-DIMITRIOU, X.-PAPANASTASSIOU, N.: Basic matrix theorems for I-convergence in (l)-groups, Math. Slovaca (2011), to appear.10.2478/s12175-012-0053-6Search in Google Scholar

[9] BOCCUTO, A.-RIEˇCAN, B.-VR´ABELOV´A, M.: Kurzweil-Henstock Integral in Riesz Spaces. Bentham Science Publ., USA, Oak Park, IL, 2009.Search in Google Scholar

[10] DEMARR, R. E.: Order convergence and topological convergence, Proc. Amer. Math. Soc. 16 (1965), 588-590.10.1090/S0002-9939-1965-0178449-3Search in Google Scholar

[11] DIMITRIOU, X.-BOCCUTO, A.-PAPANASTASSIOU, N.: Schur and matrix theo- rems with respect to I-convergence, in: Proc. 13th Greek Math. Anal. Conf., Ioaninna, June 2010, to appear.Search in Google Scholar

[12] FREEDMAN, A. R.-SEMBER, J. J.: Densities and summability, Pacific J. Math. 95 (1981), 293-305.10.2140/pjm.1981.95.293Search in Google Scholar

[13] FRIDY, J. A.: On statistical convergence, Analysis 5 (1985), 301-313.10.1524/anly.1985.5.4.301Search in Google Scholar

[14] HENRIKSEN, M.: Multiplicative summability methods and the Stone-ˇCech compactifica- tion, Math. Zeitschr. 71 (1959), 427-435.10.1007/BF01181414Search in Google Scholar

[15] KOSTYRKO, P.-ˇ SAL´A T, T.-WILCZY´NSKI, W.: I-convergence, Real Anal. Exch. 26 (2000/2001), 669-685.10.2307/44154069Search in Google Scholar

[16] MAY, R. W.-MCARTHUR, C. W.: Comparison of two types of order convergence with topological convergence in an ordered topological vector space, Proc. Amer. Math. Soc. 63 (1977), 49-55.10.1090/S0002-9939-1977-0438078-9Search in Google Scholar

[17] RIEˇCAN, B.-NEUBRUNN, T.: Integral, Measure and Ordering. Kluwer Acad. Publ., Dordrecht, 1997; Ister Science, Bratislava, 1997.10.1007/978-94-015-8919-2Search in Google Scholar

ISSN:
1210-3195
Language:
English
Publication timeframe:
3 times per year
Journal Subjects:
Mathematics, General Mathematics