On the relationship between the dimension of the Lebesgue-Stieltjes measure and the rate of approximation of a function by step functions (Q721817)
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scientific article; zbMATH DE number 6908956
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the relationship between the dimension of the Lebesgue-Stieltjes measure and the rate of approximation of a function by step functions |
scientific article; zbMATH DE number 6908956 |
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On the relationship between the dimension of the Lebesgue-Stieltjes measure and the rate of approximation of a function by step functions (English)
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20 July 2018
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The author studies the relationship between the Hausdorff dimension of the corresponding Lebesgue-Stieltjes measure and the rate of approximation of a monotone function by step functions. In terms of the approximation rate an upper bound on the dimension is obtained. Moreover, it is proved that a lower bound cannot be constructed in these terms.
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Lebesgue-Stieltjes measure
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Hausdorff dimension
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rate of approximation
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