Metrization of the space of weakly additive positively-homogeneous functionals. (English) Zbl 1379.46011

The author describes an analog of the Kantorovich-Rubinstein transport metric and topological and geometric properties of weakly additive order-preserving normalized functionals. Namely he asserts that the functor of weakly additive order preserving positively homogeneous functionals is metrizable.


46A55 Convex sets in topological linear spaces; Choquet theory
Full Text: DOI


[1] Albeverio, S.; Ayupov, A. Sh.; Zaitov, A. A., On certain properties of the space of order-preserving functionals, Topol. Appl., 155, 1792-1799, (2008) · Zbl 1163.46019
[2] Alkins, R.; Valov, V., Functional extenders and set-valued retractions, J. Math. Anal. Appl., 399, 306-314, (2013) · Zbl 1258.54002
[3] Bogachev, V. I., Measure theory, vol. II, (2007), Springer-Verlag Berlin, Heidelberg · Zbl 1120.28001
[4] Djabbarov, G. F., Description of extremal points of the space of weakly additive positively-homogeneous functionals of the two-point set, Uzbek. Mat. Zh., 3, 17-25, (2005)
[5] Djabbarov, G. F., Categorical properties of the functor of weakly additive positively-homogeneous functionals, Uzbek. Mat. Zh., 2, 20-28, (2006)
[6] Fedorchuk, V. V., Triples of infinite iterates of metrizable functors, Math. USSR, Izv., Izv. Akad. Nauk SSSR, Ser. Mat., 54, 2, 396-417, (1990), (English. Russian original), translation from:
[7] Kantorovich, L. V.; Rubinstein, G. Sh., On a functional space and certain extremal problems, Dokl. Akad. Nauk SSSR, 115, 1058-1061, (1957), (in Russian) · Zbl 0081.11501
[8] Kantorovich, L. V.; Rubinstein, G. Sh., On a space of completely additive functions, Vestn. Leningr. Univ., Math., 13, 52-59, (1958), (in Russian) · Zbl 0082.11001
[9] Karchevska, L.; Radul, T., On extension of functors, Comment. Math. Univ. Carol., 53, 269-279, (2012) · Zbl 1265.18010
[10] Kudaybergenov, K. K.; Begjanova, K. U., Description of weakly additive order-preserving functionals on the plane, Vladikavkaz. Math. J., 13, 31-37, (2011) · Zbl 1225.46023
[11] Radul, T., On the functor of order-preserving functionals, Comment. Math. Univ. Carol., 39, 3, 609-615, (1998) · Zbl 0962.54009
[12] Sadovnichii, Yu. V., Lifting the functors \(U_\tau\) and \(U_R\) to the categories of bounded metric spaces and uniform spaces, Sb. Math., 191, 1667-1691, (2000) · Zbl 1029.54037
[13] Shapiro, L. B., On function extension operators and normal functors, Vestn. Mosk. Univ., 1, 35-42, (1992), (in Russian) · Zbl 0810.54019
[14] Zaitov, A. A., Open mapping theorem for spaces of weakly additive homogeneous functionals, Math. Notes, 88, 655-660, (2011) · Zbl 1236.46034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.