Yuanzhe Shi

Local Scaling and Dimension Distortion of Generalized Cantor Functions

Let \(\mu\) be a self-similar Cantor measure on \(\mathbb R\) associated with a probability weight vector \(\mathbf p\), let \(K=\operatorname{supp}\mu\), and let \(F\) denote the distribution function of \(\mu\). We characterize the points \(x\in K\) at which the local scaling exponent \[ \lim_{\substack{y\to x, y\in...