Geodesic
Metrization of the space of weakly additive order-preserving homogeneous functionals
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 88-94

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The work is devoted to the study of the space of weakly additive, order-preserving, normalized, and homogeneous functionals on a compact metric space. For a metric compact space $X$, we propose a formula for calculating the Kantorovich–Rubinstein metric on the space of weakly additive, order-preserving, homogeneous functionals $S(X)$. Also, we prove that the superextension $\lambda(X)$ of the compact set $X$ is isometrically embedded in the space $S(X)$.
Keywords: weakly additive functional, Kantorovich–Rubinstein metric, hyperspace, superextension. 
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     author = {G.F.Djabbarov and M. M. Jabborov},
     title = {Metrization of the space of weakly additive order-preserving homogeneous functionals},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {88--94},
     publisher = {mathdoc},
     volume = {197},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_197_a9/}
}
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G.F.Djabbarov; M. M. Jabborov. Metrization of the space of weakly additive order-preserving homogeneous functionals. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 88-94. http://geodesic.mathdoc.fr/item/INTO_2021_197_a9/