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On a construction of J. Tkadlec concerning \(\sigma\)-porous sets. (English) Zbl 1009.28009

Summary: In the paper, in Real Anal. Exch. 12(1986/87), 349-353 (1987; Zbl 0649.28005), J. Tkadlec gave an example of a finite singular Borel measure \(\mu\) on the real line such that all \(\sigma\)-porous sets are of \(\mu\)-measure zero. We give an alternative proof, i.e., probably a simpler construction, of his theorem (loc. cit.) and we also give a similar example in \(\mathbb{R}^n\).

MSC:

28A35 Measures and integrals in product spaces
28A12 Contents, measures, outer measures, capacities
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets

Citations:

Zbl 0649.28005
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