**"****Dimensional and Dimensionless Sets****"**

By

**ALEXANDER GONCHAROV**

**(BİLKENT UNIVERSITY)**

**Abstract:
** An increasing continuous function **h **on
the set of nonnegative real numbers with **h(0)=0** is called a dimension
function. A set in a metric space is called *dimensional *if its**
h**-Hausdorff measure is
positive and finite for some dimension function **h. **The first
nontrivial example of dimensionless set
was presented by E.Best in 1939. We
consider this example and recent results by L.Olsen about dimensionability of the set of Liouville
numbers.

**Date: ****Tuesday, September 23, 2014**

**Time: ****16:00**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.