Geodesic
Convergence theorems for measures with values in Riesz spaces
Kybernetika, Tome 38 (2002) no. 3, pp. 287-295 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 28B15, 46G10
Keywords: convergence theorem; Riesz space; Lebesgue decomposition 
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Candeloro, Domenico. Convergence theorems for measures with values in Riesz spaces. Kybernetika, Tome 38 (2002) no. 3, pp. 287-295. http://geodesic.mathdoc.fr/item/KYB_2002_38_3_a5/

[1] Boccuto A.: Vitali–Hahn–Saks and Nikodým theorems for means with values in Riesz spaces. Atti Sem. Mat. Fis. Univ. Modena 44 (1996), 157–173 | MR | Zbl

[2] Boccuto A.: Dieudonné-type theorems for means with values in Riesz spaces. Tatra Mountains Math. Publ. 8 (1996), 29–42 | MR | Zbl

[3] 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 | DOI | MR | Zbl

[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 | MR | Zbl

[5] Boccuto A., Candeloro D.: Dieudonné-type theorems for set functions with values in $(l)$-groups. Real Anal. Exchange, to appear | MR | Zbl

[6] Brooks J. K.: On the Vitali-Hahn-Saks and Nikodým theorems. Proc. Nat. Acad. Sci. U. S. A. 64 (1969), 468–471 | DOI | MR | Zbl

[7] Brooks J. K.: Equicontinuous sets of measures and applications to Vitali’s integral convergence theorem and control measures. Adv. in Math. 10 (1973), 165–171 | DOI | MR | Zbl

[8] Brooks J. K.: On a theorem of Dieudonné. Adv. in Math. 36 (1980), 165–168 | DOI | MR | Zbl

[9] Candeloro D., Letta G.: Sui teoremi di Vitali–Hahn–Saks e di Dieudonné. Rend. Accad. Naz. Sci. XL 9 (1985), 203–213 | MR

[10] Inglesias M. Congost: Medidas y probabilidades en estructuras ordenadas. Stochastica 5 (1981), 45–48 | MR

[11] Dieudonné J.: Sur la convergence des suites de mesures de Radon. An. Acad. Brasil. Cienc. 23 (1951), 21–38; 277–282 | MR | Zbl

[12] Nikodým O.: Sur les suites convergentes de fonctions parfaitement additives d’ensemble abstrait. Monatsc. Math. 40 (1933), 427–432 | DOI | MR | Zbl

[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 | MR | Zbl

[15] Schmidt K.: Decompositions of vector measures in Riesz spaces and Banach lattices. Proc. Edinburgh Math. Soc. 29 (1986), 23–39 | MR | Zbl