Chan, Vincent2010-08-252010-08-252010-08-252010http://hdl.handle.net/10012/5369We prove that if $1 > \alpha > 1/2$, then there exists a probability measure $\mu$ such that the Hausdorff dimension of its support is $\alpha$ and $\mu*\mu$ is a Lipschitz function of class $\alpha-1/2$.enconvolution squaresingular measureLipschitzHausdorff dimensionMaster ThesisPure Mathematics