Hausdorff Measure Properties of the Asymmetric Cauchy Processes

Abstract

The function $\varphi(h) = h/|\log h|$ is shown to be an exact Hausdorff measure function for the range of all strictly asymmetric Cauchy processes in $R^k, k \geqq 2$. The same function is also shown to correctly measure the graph of any strictly asymmetric Cauchy process.