On Riemann sums (Q418224)
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scientific article; zbMATH DE number 6038700
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Riemann sums |
scientific article; zbMATH DE number 6038700 |
Statements
On Riemann sums (English)
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28 May 2012
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modified Riemann sums
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continuous functions
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exact derivatives
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Henstock-Kurzweil integral
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change of variables
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Continuous functions and exact derivatives are characterized in terms of modified Riemann sums: NEWLINE\[NEWLINE \sum\limits_{i=1}^{n}f(\xi_i)(x_i - x_{i-1}), NEWLINE\]NEWLINE where the sequence of points \(x_0,x_1,\dots ,x_n\) is not assumed to be increasing. Applications of the sums to the change of variable formulas are given.
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