Franklin Mendivil, Acadia University
“Hausdorff and packing measures of Cantor sets associated with series”
Given a convergent infinite series of positive terms an, the set of all possible subsums forms a perfect and compact set. If in addition the series satisfies a fast decay condition, the resulting set, Ca, is totally disconnected.
Manual Mora ́n studied these Ca, extended the construction to Rd, and gave some results on the Hausdorff dimension and measure. In this talk, I will discuss our (slight) extension of his construction and present results regarding the Hausdorff and packing dimension and measure of Ca. I will also present some results concerning the existence of subsets of Ca of a given (smaller) dimension and measure. In particular, we show that for all d < dim(Ca) there exist a subsequence bn of an with dim(Cb) = d.
This is joint work with Kathryn Hare and Leandro Zuberman.