%0 Journal Article
%A Mera Rivas, María Eugenia
%A Morán Cabré, Manuel
%A Preiss, David
%A Zajicek, Ludik
%T Porosity, σ-porosity and measures
%D 2003
%@ 0951-7715
%U https://hdl.handle.net/20.500.14352/60449
%X 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.
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