On the Hausdorff dimension of countable intersections of certain sets of normal numbers
Mar 7 2013 – 3:00pm – 4:00 pm
William Mance (University of North Texas)
We show that the set of numbers that are Q-distribution normal but not simply Q-ratio normal has full Hausdorff dimension. We further show under some conditions that countable intersections of sets of this form still have full Hausdorff dimension even though they are not winning sets (in the sense of W. Schmidt). As a consequence of this, we construct many explicit examples of numbers that are simultaneously distribution normal but not simply ratio normal with respect to certain countable families of basic sequences. Additionally, we prove that some related sets are either winning sets or sets of the first category.