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Attainable values for upper porosities of measures

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2000
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Michigan State University Press
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In this paper we introduce two definitions of upper porosity of a measure which range from 0 to (1/2) and from 0 to 1 respectively, and prove that actually the first porosity only can take the extreme values 0 or (1/2), and the second one takes either the value 0 or the values (1/2) or 1. The other main result of this paper says that any measure μ which does not satisfy the doubling condition μ-a.e. has a maximal porosity.
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