Stability of quantization dimension and quantization for homogeneous Cantor measures

• Autores: Marc Kesseböhmer, Sanguo Zhu
• Localización: Mathematische Nachrichten, ISSN 0025-584X, Vol. 280, Nº. 8, 2007, págs. 866-881
• Idioma: inglés
• DOI: 10.1002/mana.200410519
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• Resumen

  • 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)