caa a22 4500 44586902X CHVBK 20180317145506.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00605-009-0176-1 doi (NATIONALLICENCE)springer-10.1007/s00605-009-0176-1 Zhu Sanguo School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074, Wuhan, China aut The quantization dimension of the self-affine measures on general Sierpiński carpets [Elektronische Daten] [Sanguo Zhu] Letμ be a self-affine measure on a general Sierpiński carpet E. We give a characterization for the upper and lower quantization dimension ofμ in terms of revised cylinder sets. Using this characterization, we prove that the quantization dimension D r(μ) ofμ exists for all r > 0 under an additional condition. We establish an explicit formula for D r(μ) and show that it increases to the box-counting dimension $${dim_B^* \mu}$$ ofμ as r tends to infinity. For a class of Sierpiński carpets E and the uniform measuresμ on E, we show that the quantization dimension ofμ coincides with its box-counting dimension and that the D r(μ)-dimensional upper and lower quantization coefficient ofμ are both positive and finite. Springer-Verlag, 2009 Quantization dimension nationallicence Quantization coefficient nationallicence Self-affine measure nationallicence Sierpiński carpets nationallicence Finite maximal anti-chain nationallicence Monatshefte für Mathematik Springer Vienna 162/3(2011-03-01), 355-374 0026-9255 162:3<355 2011 162 605 https://doi.org/10.1007/s00605-009-0176-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-009-0176-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zhu Sanguo School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074, Wuhan, China aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 162/3(2011-03-01), 355-374 0026-9255 162:3<355 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer