"Dimensional and Dimensionless Sets"
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
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.