Geodesic
On the Riesz Integral Representation of Additive Set-Valued Maps (II)
Journal of convex analysis, Tome 26 (2019) no. 4, pp. 1053-1058
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

Let T be a compact topological space, and let C+(T) be the space of all non-negative continuous real-valued functions defined on T endowed with the topology of uniform convergence. We prove the Riesz integral representation for continuous additive and positive set-valued maps defined on C+(T) with values in the space cc(E) of all weakly compact convex non-empty subsets of a Banach space E. As an application we give a generalization of Dunford-Schwartz's result on the Riesz integral representation for any continuous set-valued map (not necessary positive).
Classification : 28B20, 54C60
Mots-clés : Linear maps, set-valued maps, set-valued measures, topology 
@article{JCA_2019_26_4_JCA_2019_26_4_a0,
     author = {A. K. Lakmon and K. Musial},
     title = {On the {Riesz} {Integral} {Representation} of {Additive} {Set-Valued} {Maps} {(II)}},
     journal = {Journal of convex analysis},
     pages = {1053--1058},
     year = {2019},
     volume = {26},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2019_26_4_JCA_2019_26_4_a0/}
}
TY  - JOUR
AU  - A. K. Lakmon
AU  - K. Musial
TI  - On the Riesz Integral Representation of Additive Set-Valued Maps (II)
JO  - Journal of convex analysis
PY  - 2019
SP  - 1053
EP  - 1058
VL  - 26
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JCA_2019_26_4_JCA_2019_26_4_a0/
ID  - JCA_2019_26_4_JCA_2019_26_4_a0
ER  - 
%0 Journal Article
%A A. K. Lakmon
%A K. Musial
%T On the Riesz Integral Representation of Additive Set-Valued Maps (II)
%J Journal of convex analysis
%D 2019
%P 1053-1058
%V 26
%N 4
%U http://geodesic.mathdoc.fr/item/JCA_2019_26_4_JCA_2019_26_4_a0/
%F JCA_2019_26_4_JCA_2019_26_4_a0
A. K. Lakmon; K. Musial. On the Riesz Integral Representation of Additive Set-Valued Maps (II). Journal of convex analysis, Tome 26 (2019) no. 4, pp. 1053-1058. http://geodesic.mathdoc.fr/item/JCA_2019_26_4_JCA_2019_26_4_a0/