Microscopic sets

Grazyna Horbaczewska - Lodz

Luns 8 e martes 9 de xuño de 2015 ás 16 horas na aula 7.

Our purpose is to present some fields of research undertaken lately at the University of Lodz.

The notion of microscopic set is presented. We look more closely at the definition, discuss some examples and basic properties.

We review some of the standard facts on the notion of a sigma-ideal with examples and then we compare the family of microscopicd sets with other sigma-ideals like Lebesgue null sets, sets of universal measure zero, sets of strong measure zero, sets of Hausdorff dimension zero.

Applications in measure theory are concerned.

We proceed with the study of possibility of improving some classical theorems with the use of microscopic sets.

We touch generalizations of the notion of microscopic sets.

Discussion of possible directions of developing research on the studied topic.

© Grazyna Horbaczewska.