"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.