Mixed L~q-Dimensions And Divergence Points Of Measures

In this dissertation, we mainly study the Mixed L~q -dimensions of finite measures and the packing dimension of the set of the mixed divergence points of self-similar measures.In Chapter 1, we briefly review the fractal naissance and give some fundamental concepts and properties of the strong separation condition and the fractal dimensions which conclude Hausdorff dimension, box dimension, packing dimension and measure dimension.In Chapter 2, we mainly discuss the typical behavior of the lower L~q-dimension of a single measure for