On the topologies generated by the sequences of measurable sets tending to zero

09 Xul 2024
17:00
Aula 7, Facultade de Matemáticas (USC) e en liña (MS Teams)
CITMAga

"On the topologies generated by the sequences of measurable sets tending to zero", organizado por CITMAga. Será impartido por Jacek Hejduk (Faculty of Mathematics and Computer Science, University of Lodz, Polonia).

Data: Martes 9 de xullo

Hora: 17:00 h.

Duración: 1 hora

Lugar: Aula 7, Facultade de Matemáticas (USC) e en liña (MS Teams)

Abstract:
Let {Sn} be a sequence of Lebesgue measurable sets on R converging to zero; i.e., diam(Sn U {0}) converges to 0 as n goes to infinity. Defining for every measurable set A, F(A) = {x in R :çlimn (l(AÇ(x+Sn))/l(Sn) = 1}, we consider in the family L of Lebesgue measurable sets a family T F = {A in L : A is contained in F(A)}. This family is a topology where some properties are regulated by the structure of the sequence {Sn}.