Jan Severin Reimann, Thesis Supervisor Stephen George Simpson, Thesis Honors Advisor
Keywords:
Cantor set Hausdorff measure Kolmogorov complexity
Abstract:
This thesis is motivated by the general construction of Cantor sets and the Hausdorff measure of Cantor sets corresponding to different series. We provide background knowledge on the Cantor set and Hausdorff measure, and apply it to the $p$-series and geometric series on Cantor space, extending the previous work by Cabrelli et al. In the last chapter, we exhibit a construction of a Cantor set associated with Kolmogorov complexity which has Hausdorff dimension 1.
