Geodesic
Quantization dimension of probability measures
Sbornik. Mathematics, Tome 215 (2024) no. 8, pp. 1043-1052 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The quantization dimension of a probability measure defined on a metric compact space $X$ is known not to exceed the box dimension of its support. It is proved that on any metric compact space of box dimension $\dim_BX=a\leq\infty$, for arbitrary two numbers $b\in[0,a]$ and $c\in[b,a]$ there is a probability measure such that its lower quantization dimension is $b$ and its upper quantization dimension is $c$. Bibliography: 6 titles.
Keywords: space of probability measures, intermediate value theorem for the quantization dimension.
Mots-clés : box dimension, quantization dimension 
@article{SM_2024_215_8_a1,
     author = {A. V. Ivanov},
     title = {Quantization dimension of probability measures},
     journal = {Sbornik. Mathematics},
     pages = {1043--1052},
     year = {2024},
     volume = {215},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_8_a1/}
}
TY  - JOUR
AU  - A. V. Ivanov
TI  - Quantization dimension of probability measures
JO  - Sbornik. Mathematics
PY  - 2024
SP  - 1043
EP  - 1052
VL  - 215
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_2024_215_8_a1/
LA  - en
ID  - SM_2024_215_8_a1
ER  - 
%0 Journal Article
%A A. V. Ivanov
%T Quantization dimension of probability measures
%J Sbornik. Mathematics
%D 2024
%P 1043-1052
%V 215
%N 8
%U http://geodesic.mathdoc.fr/item/SM_2024_215_8_a1/
%G en
%F SM_2024_215_8_a1
A. V. Ivanov. Quantization dimension of probability measures. Sbornik. Mathematics, Tome 215 (2024) no. 8, pp. 1043-1052. http://geodesic.mathdoc.fr/item/SM_2024_215_8_a1/

[1] S. Graf and H. Luschgy, Foundations of quantization for probability distributions, Lecture Notes in Math., 1730, Springer-Verlag, Berlin, 2000, x+230 pp. | DOI | MR | Zbl

[2] A. V. Ivanov, “On the functor of probability measures and quantization dimensions”, Vestn. Tomsk. Gos. Univ., Mat. Mekh., 2020, no. 63, 15–26 (Russian) | DOI | MR | Zbl

[3] A. V. Ivanov, “On the range of the quantization dimension of probability measures on a metric compactum”, Siberian Math. J., 63:5 (2022), 903–908 | DOI | MR | Zbl

[4] A. V. Ivanov, “On the intermediate values of the box dimensions”, Siberian Math. J., 64:3 (2023), 593–597 | DOI | MR | Zbl

[5] V. V. Fedorchuk and V. V. Filippov, General topology. Basic constructions, Publishing House of Moscow State University, Moscow, 1988, 253 pp. (Russian) | Zbl

[6] Ya. B. Pesin, Dimension theory in dynamical systems: contemporary views and applications, Chicago Lectures in Math., Univ. Chicago Press, Chicago, 1997, xi+304 pp. | DOI | MR | Zbl