RT Journal Article
T1 Porosity, σ-porosity and measures
A1 Mera Rivas, María Eugenia
A1 Morán Cabré, Manuel
A1 Preiss, David
A1 Zajicek, Ludik
AB We show that given a σ-finite Borel regular measure μ in a metric space X, every σ-porous subset of X of finite measure can be approximated by strongly porous sets. It follows that every σ-porous set is the union of a σ-strongly porous set and a μ-null set. This answers in the positive the question whether a measure which is absolutely continuous with respect to the σ-ideal of all σ-strongly porous sets is absolutely continuous with respect to the σ-ideal of all σ-porous sets. Using these results, we obtain a natural decomposition of measures according to their upper porosity and obtain detailed information on values that upper porosity may attain almost everywhere.
PB American Physical Society
SN 0951-7715
YR 2003
FD 2003
LK https://hdl.handle.net/20.500.14352/60449
UL https://hdl.handle.net/20.500.14352/60449
LA eng
DS Docta Complutense
RD 9 may 2025