Study Of Quantization Dimension

In this dissertation,we mainly study properties of quantization dimension, including comparison to other dimensions of measures,and study the quantization dimension of probability measure supported on statistically self-similar with strong separation condition.In Chapter 1,we briefly review the fractal naissance and give some fundamental concepts,properties of the fractal dimensions and measure theory.In Chapter 2,we mainly study the equivalent definition of quantization dimension of measures and compare it to other dimensions of measures.In Chapter 3,we mainly study the quantization dimension of probability measure supported on statistically self-similar set.We establish a relationship between the quantization dimension of probability measure.In Chapter 4,we mainly study the formula of the quantization dimension and other dimensions of some measures.We compare the quantity relation of these dimensions.In Chapter 5,we mainly define measure's exact upper dimension by there different angles.They are equivalent.And we study the relation between measure's exact upper dimension and point dimension.