On the Čech-Completeness of the Space of τ-Smooth Idempotent Probability Measures

被引：0

作者：

Kocinac, Ljubisa D. R. ^{[1
,2
]}

Zaitov, Adilbek A. ^{[3
]}

Eshimbetov, Muzaffar R. ^{[4
,5
]}

机构：

[1] Univ Nis, Fac Sci & Math, Nish 18000, Serbia

[2] State Univ Novi Pazar, Dept Math, Novi Pazar 36300, Serbia

[3] Tashkent Univ Architecture & Civil Engn, Dept Math & Nat Disciplines, Yangi Shahar Str 9, Tashkent 100194, Uzbekistan

[4] Uzbek Acad Sci, VI Romanovskiy Inst Math, Univ Str 9, Tashkent 100174, Uzbekistan

[5] Tashkent Int Univ Financial Management & Technol, Dept Math, Amir Temur Str 15, Tashkent 100047, Uzbekistan

来源：

AXIOMS | 2024年 / 13卷 / 08期

关键词：

& Ccaron; ech-complete space; compact space; probability measure; tau-smooth idempotent probability measure; neighbourhood system; FUNCTOR;

D O I：

10.3390/axioms13080569

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the set I(X) of probability measures on a compact Hausdorff space X, we propose a new way to introduce the topology by using the open subsets of the space X. Then, among other things, we give a new proof that for a compact Hausdorff space X, the space I(X) is also a compact Hausdorff space. For a Tychonoff space X, we consider the topological space I-tau(X) of tau-smooth idempotent probability measures on X and show that the space I-tau(X) is & Ccaron;ech-complete if and only if the given space X is & Ccaron;ech-complete.

引用

页数：13

共 50 条

[31] Completeness of the space of separable measures in the Kantorovich-Rubinshtein metric
Kravchenko, AS
SIBERIAN MATHEMATICAL JOURNAL, 2006, 47 (01) : 68 - 76
[32] ON THE DYNAMICS OF INDUCED MAPS ON THE SPACE OF PROBABILITY MEASURES
Bernardes, Nilson C., Jr.
Vermersch, Romulo M.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 368 (11) : 7703 - 7725
[33] EXTREMAL FUNCTIONALS IN A SPACE OF PROBABILITY-MEASURES
RACHEV, ST
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1987, 31 (03) : 540 - 540
[34] Cubic Hermite interpolators on the space of probability measures
Adouani, Ines
Samir, Chafik
Tran, Tien Tam
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (18) : 13813 - 13832
[35] On the strong regularity with the multifractal measures in a probability space
Bilel Selmi
Analysis and Mathematical Physics, 2019, 9 : 1525 - 1534
[36] Dynamics of Induced Maps on the Space of Probability Measures
Shao, Hua
Zhu, Hao
Chen, Guanrong
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2022, 34 (02) : 961 - 981
[37] Hilbert space embeddings and metrics on probability measures
Sriperumbudur, Bharath K.
Gretton, Arthur
Fukumizu, Kenji
Schölkopf, Bernhard
Lanckriet, Gert R. G.
Journal of Machine Learning Research, 2010, 11 : 1517 - 1561
[38] Ergodic decomposition of probability measures on the configuration space
Shimomura, H
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1995, 35 (04): : 611 - 630
[39] A note on the Poisson structures of the space of probability measures
Shishido, Yuichi
MATHEMATISCHE NACHRICHTEN, 2007, 280 (16) : 1827 - 1833
[40] Geodesics for a class of distances in the space of probability measures
Cardaliaguet, P.
Carlier, G.
Nazaret, B.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2013, 48 (3-4) : 395 - 420

← 1 2 3 4 5 →