Convergence theorems for measures with values in Riesz spaces

Domenico Candeloro

Kybernetika (2002)

  • Volume: 38, Issue: 3, page [287]-295
  • ISSN: 0023-5954

Abstract

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In some recent papers, results of uniform additivity have been obtained for convergent sequences of measures with values in l -groups. Here a survey of these results and some of their applications are presented, together with a convergence theorem involving Lebesgue decompositions.

How to cite

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Candeloro, Domenico. "Convergence theorems for measures with values in Riesz spaces." Kybernetika 38.3 (2002): [287]-295. <http://eudml.org/doc/33583>.

@article{Candeloro2002,
abstract = {In some recent papers, results of uniform additivity have been obtained for convergent sequences of measures with values in $l$-groups. Here a survey of these results and some of their applications are presented, together with a convergence theorem involving Lebesgue decompositions.},
author = {Candeloro, Domenico},
journal = {Kybernetika},
keywords = {convergence theorem; Riesz space; Lebesgue decomposition; convergence theorem; Riesz space; Lebesgue decomposition},
language = {eng},
number = {3},
pages = {[287]-295},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Convergence theorems for measures with values in Riesz spaces},
url = {http://eudml.org/doc/33583},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Candeloro, Domenico
TI - Convergence theorems for measures with values in Riesz spaces
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 3
SP - [287]
EP - 295
AB - In some recent papers, results of uniform additivity have been obtained for convergent sequences of measures with values in $l$-groups. Here a survey of these results and some of their applications are presented, together with a convergence theorem involving Lebesgue decompositions.
LA - eng
KW - convergence theorem; Riesz space; Lebesgue decomposition; convergence theorem; Riesz space; Lebesgue decomposition
UR - http://eudml.org/doc/33583
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., Candeloro D., 10.1006/jmaa.2001.7715, J. Math. Anal. Appl. 265 (2002), 170–194 Zbl1006.28012MR1874264DOI10.1006/jmaa.2001.7715
  4. Boccuto A., Candeloro D., Vitali and Schur-type theorems for Riesz-space-valued set functions, Atti Sem. Mat. Fis. Univ. Modena 50 (2002), 85–103 Zbl1096.28006MR1910780
  5. Boccuto A., Candeloro D., Dieudonné-type theorems for set functions with values in ( l ) -groups, Real Anal. Exchange, to appear Zbl1067.28011MR1922663
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  7. Brooks J. K., 10.1016/0001-8708(73)90104-7, Adv. in Math. 10 (1973), 165–171 (1973) Zbl0249.28009MR0320268DOI10.1016/0001-8708(73)90104-7
  8. Brooks J. K., 10.1016/0001-8708(80)90014-6, Adv. in Math. 36 (1980), 165–168 (1980) Zbl0441.28006MR0574646DOI10.1016/0001-8708(80)90014-6
  9. Candeloro D., Letta G., Sui teoremi di Vitali–Hahn–Saks e di Dieudonné, Rend. Accad. Naz. Sci. XL 9 (1985), 203–213 (1985) MR0899250
  10. Inglesias M. Congost, Medidas y probabilidades en estructuras ordenadas, Stochastica 5 (1981), 45–48 (1981) MR0625841
  11. Dieudonné J., Sur la convergence des suites de mesures de Radon, An. Acad. Brasil. Cienc. 23 (1951), 21–38; 277–282 (1951) Zbl0044.12004MR0042496
  12. Nikodým O., 10.1007/BF01708880, Monatsc. Math. 40 (1933), 427–432 (1933) Zbl0008.25003MR1550217DOI10.1007/BF01708880
  13. Luxemburg W. A. J., Zaanen A. C., Riesz Spaces, I, North–Holland, Amsterdam 1971 
  14. Riečan B., Neubrunn T., Integral, Measure and Ordering, Kluwer Academic Publishers / Ister Science, Bratislava 1997 Zbl0916.28001MR1489521
  15. Schmidt K., Decompositions of vector measures in Riesz spaces and Banach lattices, Proc. Edinburgh Math. Soc. 29 (1986), 23–39 (1986) Zbl0569.28011MR0829177

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