Publication: Porosity, σ-porosity and measures
Full text at PDC
Advisors (or tutors)
American Physical Society
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.