✦ LIBER ✦

Stability of quantization dimension and quantization for homogeneous Cantor measures

✍ Scribed by Marc Kesseböhmer; Sanguo Zhu

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 207 KB
Volume: 280
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200410519

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We effect a stabilization formalism for dimensions of measures and discuss the stability of upper and lower quantization dimension. For instance, we show for a Borel probability measure with compact support that its stabilized upper quantization dimension coincides with its packing dimension and that the upper quantization dimension is finitely stable but not countably stable. Also, under suitable conditions explicit dimension formulae for the quantization dimension of homogeneous Cantor measures are provided. This allows us to construct examples showing that the lower quantization dimension is not even finitely stable. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Optimal quantization for dyadic homogene

Optimal quantization for dyadic homogeneous Cantor distributions

✍ Wolfgang Kreitmeier 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 243 KB

## Abstract For a large class of dyadic homogeneous Cantor distributions in ℝ, which are not necessarily self‐similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non‐existence of the quantization coefficient. The class