Construction of a finite Borel measure with \(\sigma\)-porous sets as null sets (Q1105721)
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scientific article; zbMATH DE number 4059755
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Construction of a finite Borel measure with \(\sigma\)-porous sets as null sets |
scientific article; zbMATH DE number 4059755 |
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Construction of a finite Borel measure with \(\sigma\)-porous sets as null sets (English)
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1987
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The main result of the paper is the following theorem: There exists a finite Borel measure on the real line that is zero on every sigma porous set and it not absolutely continuous with respect to Lebesgue measure. The author uses in the construction his earlier results on porous sets [Real Anal. Exch. 9, 473-482 (1984; Zbl 0582.28001)].
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absolute continuity with respect to Lebesgue measure
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finite Borel measure
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sigma porous set
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