Mera, M. Eugenia; Morán, Manuel Attainable values for upper porosities of measures. (English) Zbl 1023.28002 Real Anal. Exch. 26(2000-2001), No. 1, 101-115 (2001). To a measure \(\mu\) over \(\mathbb R^{n}\) one associates the upper and lower porosity, denoted \(\overline{p}(\mu)\), respectively \(\underline{p}(\mu)\), in terms of the upper, respectively lower porosity of all subsets in \(\mathbb R^{n}\) of positive \(\mu\)-measure. The main result of the paper is that upper porosity of a Radon probability measure on \(\mathbb R^{n}\) is either \(0\) or \(1/2\).The authors introduce a second definition of upper porosity, denoted \(\overline{\text{por}}(\mu)\), which in the case of measures satisfying the so-called doubling condition is equivalent to the first one. It is proved that for a Radon probability measure, \(\overline{\text{por}}(\mu)\) is \(0, 1/2\) or \(1\). Reviewer: Emilia Petrisor (Timişoara) Cited in 1 ReviewCited in 4 Documents MSC: 28A12 Contents, measures, outer measures, capacities 28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets Keywords:measures satisfying the doubling condition; porosity of sets; porosity of measures × Cite Format Result Cite Review PDF