Quantization for probability measures [Elektronische Ressource] / von Sanguo Zhu

Quantization for probability measuresvon Sanguo ZhuDissertationzur Erlangung des Grades eines Doktors derNaturwissenschaften– Dr. rer. nat. –Vorgelegt im Fachbereich 3 (Mathematik & Informatik)der Universität Bremenim September 2005Datum des Promotionskolloquiums: 7. Dezember 2005.Gutachter: Prof. Dr. Marc Kesseböhmer (Universität Bremen)Prof. Dr. Siegfried Graf (Universität Passau)ContentsAbstract 5Introduction 7Chapter 1. Quantization numbers and limit quantization dimensions 131.1. Quantization numbers 131.2. Rate distortion dimension 151.3. Quantization dimension for product measures 161.4. Essential covering rate and the upper quantization dimension 171.5. Essential covering rate and limit quantization dimensions 25Chapter 2. Stability and stabilization of the upper quantization dimension 312.1. Preliminary concepts and facts 312.2. Stability and stabilization of dimensions for measures 332.3. Finite stability of the upper quantization dimension 362.4. Stabilization of the upper quantization dimension and coefficient 402.5. Quantization for homogeneous Cantor measures 452.6. Stability and stabilization of limit quantization dimension 60Chapter 3. Quantization and absolute continuity of measures 633.1. Preliminary facts 633.2. Box-counting dimension, vanishing rates and quantization 653.3. D () is not monotone and doesnot obey a variational law 72r3.4. Ahlfors-David regular measures 753.5.