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Porosity, σ-porosity and measures

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Mera Rivas, Maria Eugenia and Morán Cabré, Manuel and Preiss, David and Zajicek, Ludik (2003) Porosity, σ-porosity and measures. Nonlinearity, 16 (1). pp. 247-255. ISSN 0951-7715

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Official URL: https://doi.org/10.1088/0951-7715/16/1/315



Abstract

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.


Item Type:Article
Subjects:Sciences > Physics
Sciences > Mathematics
ID Code:58884
Deposited On:17 Feb 2020 13:36
Last Modified:17 Feb 2020 13:36

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