Geodesic
On Radon barycenters of measures on spaces of measures
The Bulletin of Irkutsk State University. Series Mathematics, Tome 44 (2023), pp. 19-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study metrizability of compact sets in spaces of Radon measures with the weak topology. It is shown that if all compacta in a given completely regular topological space are metrizable, then every uniformly tight compact set in the space of Radon measures on this space is also metrizable. It is proved that the property that compact sets of measures on a given space are metrizable is preserved for products of this space with spaces that can be embedded into separable metric spaces. In addition, we construct a Radon probability measure on the space of Radon probability measures on a completely regular space such that its barycenter is not a Radon measure.
Keywords: Radon measure, metrizable compact set of measures.
Mots-clés : barycenter 
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Vladimir I. Bogachev; Svetlana N. Popova. On Radon barycenters of measures on spaces of measures. The Bulletin of Irkutsk State University. Series Mathematics, Tome 44 (2023), pp. 19-30. http://geodesic.mathdoc.fr/item/IIGUM_2023_44_a1/

[1] Acciaio B., Beiglböck M., Pammer G., “Weak transport for non-convex costs and model-independence in a fixed-income market”, Math. Finance, 31:4 (2021), 1423–1453 | DOI

[2] Alibert J.-J., Bouchitté G., Champion T., “A new class of costs for optimal transport planning”, European J. Appl. Math., 30:6 (2019), 1229–1263 | DOI

[3] Arkhangel'ski{ĭ} A.V., Ponomarev V.I., Fundamentals of General Topology. Problems and Exercises, Translated from the Russian, Reidel, Dordrecht, 1984, 415 pp.

[4] Backhoff-Veraguas J., Beiglböck M., Pammer G., “Existence, duality, and cyclical monotonicity for weak transport costs”, Calc. Var. Partial Differ. Equ., 58:203 (2019), 1–28 | DOI

[5] Backhoff-Veraguas J., Pammer G., “Stability of martingale optimal transport and weak optimal transport”, Ann. Appl. Probab., 32:1 (2022), 721–752 | DOI

[6] Bogachev V.I., Measure Theory, In 2 vols., v. 1, Springer, Berlin, 2007, 500 pp. ; v. 2, 575 pp. | DOI

[7] Bogachev V.I., Weak Convergence of Measures, Amer. Math. Soc., Providence, Rhode Island, 2018, xii+286 pp. | DOI

[8] Bogachev V.I., “Kantorovich problems with a parameter and density constraints”, Siberian Math. J., 63:1 (2022), 34–47 | DOI

[9] Bogachev V.I., “The Kantorovich problem of optimal transportation of measures: new directions of research”, Uspehi Matem. Nauk (Russian Math. Surveys), 77:5 (2022), 3–52 (in Russian) | DOI

[10] Bogachev V.I., Malofeev I.I., “Nonlinear Kantorovich problems depending on a parameter”, The Bulletin of Irkutsk State University. Series Mathematics, 41 (2022), 96–106 | DOI

[11] Bogachev V.I., Rezbaev A.V., “Existence of solutions to the nonlinear Kantorovich problem of optimal transportation”, Mathematical Notes, 112:3 (2022), 369–377 | DOI

[12] Engelking P., General Topology, Polish Sci. Publ, Warszawa, 1977, 626 pp.

[13] Gozlan N., Roberto C., Samson P.-M., Tetali P., “Kantorovich duality for general transport costs and applications”, J. Funct. Anal., 273:11 (2017), 3327–3405 | DOI

[14] Steen L., Seebach J., Counterexamples in Topology, 2nd ed., Springer, New York, 1978, 244 pp.

[15] Topsøe F., “Preservation of weak convergence under mappings”, Ann. Math. Statist., 38:6 (1967), 1661–1665 | DOI