Hausdorff dimension of symmetric and centered sets (Q1978830)

This is an abstract of a talk about the Hausdorff dimension of subsets \(E\) of the unit interval where \(E = \bigcap E_n\); \(\{E_n\}\) is a decreasing sequence of finite intervals such that each interval from \(E_n\) contains precisely two intervals from \(E_{n+1}\) and the lengths of the intervals tend to 0. The Hausdorff dimension is given for a symmetric \(E\), an estimate for the \(s\)-dimensional Hausdorff measure is mentioned. A lower estimate of the Hausdorff dimension of a centered (in the sense of Humke) \(E\) is given.