Some new results about Brooks-Jewett and Dieudonné-type theorems in ( l ) -groups

Antonio Boccuto; Domenico Candeloro

Kybernetika (2010)

  • Volume: 46, Issue: 6, page 1049-1060
  • ISSN: 0023-5954

Abstract

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In this paper we present some new versions of Brooks-Jewett and Dieudonné-type theorems for ( l ) -group-valued measures.

How to cite

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Boccuto, Antonio, and Candeloro, Domenico. "Some new results about Brooks-Jewett and Dieudonné-type theorems in $(l)$-groups." Kybernetika 46.6 (2010): 1049-1060. <http://eudml.org/doc/196592>.

@article{Boccuto2010,
abstract = {In this paper we present some new versions of Brooks-Jewett and Dieudonné-type theorems for $(l)$-group-valued measures.},
author = {Boccuto, Antonio, Candeloro, Domenico},
journal = {Kybernetika},
keywords = {$(l)$-group; order convergence; regular measure; Brooks–Jewett theorem; Dieudonné theorem; Dieudonné theorem; -group; order convergence; regular measure; Brooks–Jewett theorem},
language = {eng},
number = {6},
pages = {1049-1060},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Some new results about Brooks-Jewett and Dieudonné-type theorems in $(l)$-groups},
url = {http://eudml.org/doc/196592},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Boccuto, Antonio
AU - Candeloro, Domenico
TI - Some new results about Brooks-Jewett and Dieudonné-type theorems in $(l)$-groups
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 6
SP - 1049
EP - 1060
AB - In this paper we present some new versions of Brooks-Jewett and Dieudonné-type theorems for $(l)$-group-valued measures.
LA - eng
KW - $(l)$-group; order convergence; regular measure; Brooks–Jewett theorem; Dieudonné theorem; Dieudonné theorem; -group; order convergence; regular measure; Brooks–Jewett theorem
UR - http://eudml.org/doc/196592
ER -

References

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  2. Boccuto, A., Dieudonné-type theorems for means with values in Riesz spaces, Tatra Mountains Math. Publ. 8 (1996), 29-42. (1996) Zbl0918.28009MR1475257
  3. Boccuto, A., Integration in Riesz spaces with respect to ( D ) -convergence, Tatra Mountains Math. Publ. 10 (1997), 33–54. (1997) Zbl0918.28010MR1469280
  4. Boccuto, A., Egorov property and weak σ -distributivity in Riesz spaces, Acta Math. (Nitra) 6 (2003), 61–66. (2003) 
  5. Boccuto, A., Candeloro, D., Dieudonné-type theorems for set functions with values in ( l ) -groups, Real Analysis Exchange 27 (2001/2002), 473–484. (2001) MR1922663
  6. Boccuto, A., Candeloro, D., 10.1006/jmaa.2001.7715, J. Math. Anal. Appl. 265 (2002), 170–194. (2002) Zbl1006.28012MR1874264DOI10.1006/jmaa.2001.7715
  7. Boccuto, A., Papanastassiou, N., Schur and Nikodym convergence-type theorems in Riesz spaces with respect to the (r)-convergence, Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia 55 (2007), 33–46. (2007) Zbl1206.28020MR2458785
  8. Brooks, J. K., 10.1016/0001-8708(80)90014-6, Adv. Math. 36 (1980), 165–168. (1980) Zbl0441.28006MR0574646DOI10.1016/0001-8708(80)90014-6
  9. Brooks, J. K., Jewett, R. S., 10.1073/pnas.67.3.1294, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 1294–1298. (1970) Zbl0216.09602MR0269802DOI10.1073/pnas.67.3.1294
  10. Candeloro, D., Sui teoremi di Vitali–Hahn–Saks, Dieudonné e Nikodým, Rend. Circ. Mat. Palermo, Ser. II 8 (1985), 439–445. (1985) MR0881420
  11. Candeloro, D., Letta, G., Sui teoremi di Vitali–Hahn–Saks e di Dieudonné, Rend. Accad. Naz. Sci. Detta dei XL 9 (1985), 203–213. (1985) MR0899250
  12. Das, R., Papanastassiou, N., Some types of convergence of sequences of real valued functions, Real Anal. Exch. 29 (2003/2004), 43–58. (2003) MR2061292
  13. Dieudonné, J., Sur la convergence des suites de mesures de Radon, An. Acad. Brasil. Ci. 23 (1951), 21–38. (1951) MR0042496
  14. Dunford, N., Schwartz, J.  T., Linear Operators I, General Theory, Interscience, New York 1958. (1958) Zbl0084.10402MR0117523
  15. Luxemburg, W. A. J., Zaanen, A. C., Riesz Spaces, I, North-Holland Publishing Co. 1971. (1971) MR0511676
  16. Riečan, B., Neubrunn, T., Integral, Measure and Ordering, Kluwer Academic Publishers, Ister Science, Bratislava 1997. (1997) MR1489521
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Citations in EuDML Documents

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  1. Antonio Boccuto, Xenofon Dimitriou, Nikolaos Papanastassiou, Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (ℓ)-group-valued measures
  2. Antonio Boccuto, Domenico Candeloro, Uniform (s)-boundedness and regularity for (l)-group-valued measures
  3. Giuseppina Barbieri, A Dieudonné theorem for lattice group-valued measures
  4. Antonio Boccuto, Xenofon Dimitriou, Dieudonné-type theorems for lattice group-valued k -triangular set functions

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