A \(\upsilon{}\)-integrable function which is not Lebesgue integrable on any portion of the unit square (Q1206291)
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scientific article; zbMATH DE number 148684
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A \(\upsilon{}\)-integrable function which is not Lebesgue integrable on any portion of the unit square |
scientific article; zbMATH DE number 148684 |
Statements
A \(\upsilon{}\)-integrable function which is not Lebesgue integrable on any portion of the unit square (English)
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1 April 1993
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For most of the generalizations of the Lebesgue integral, it is known that one can find a non-empty open subset on which the function is integrable in the ordinary Lebesgue sense. The present paper answers a question of Pfeffer by showing that an integral he has introduced, namely the so-called \(v\)-integral, does not have this property. This \(v\)- integral is defined over \(BV\) sets and is not additive.
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geometric measure
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unit square
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generalizations of the Lebesgue integral
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\(v\)-integral
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\(BV\) sets
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