On the Kluvánek construction of the Lebesgue integral with respect to a vector measure (Q2877072)
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scientific article; zbMATH DE number 6333345
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Kluvánek construction of the Lebesgue integral with respect to a vector measure |
scientific article; zbMATH DE number 6333345 |
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On the Kluvánek construction of the Lebesgue integral with respect to a vector measure (English)
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21 August 2014
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Lebesgue integral
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Riesz space
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0.89367765
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0.88390654
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0.8830521
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0.8780246
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0.86707747
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The Kluvánek construction of the Lebesgue integral of real-valued functions defined on an abstract nonempty set \(X\) with respect to a Riesz space-valued measure \(\lambda \) defined on an arbitrary ring \(A\) of subsets of \(X\) is done. The author suggests a modification of the Kluvánek construction considering first nonnegative functions only. This definition of integrals is equivalent to the Kluvánek definition in the real case and based on the representation of a nonnegative function \(f\) by a sum. The proof of the independence of integrals on this representation is the main result of this paper.
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