Geodesic
Quantization dimension of probability measures
Sbornik. Mathematics, Tome 215 (2024) no. 8, pp. 1043-1052

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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 
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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/