On the weak property of Lebesgue of \(L^1(\Omega,\Sigma,\mu)\) (Q5948876)
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scientific article; zbMATH DE number 1672118
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the weak property of Lebesgue of \(L^1(\Omega,\Sigma,\mu)\) |
scientific article; zbMATH DE number 1672118 |
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On the weak property of Lebesgue of \(L^1(\Omega,\Sigma,\mu)\) (English)
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12 November 2001
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Let \((\Omega,\Sigma,\mu)\) be a totally finite, complete and countably generated measure space. it is proved that \(L^1(\Omega,\Sigma,\mu)\) has the weak property of Lebesgue, i.e. every Riemann integrable function from a closed interval \([a,b]\) to \(L^1(\Omega,\Sigma,\mu)\) is weakly continuous almost everywhere on \([a,b]\).
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weak property of Lebesgue
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Riemann integrable function
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weakly continuous almost everywhere
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