The Lebesgue differentiation theorem via the rising sun lemma (Q1769729)
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scientific article; zbMATH DE number 2151959
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Lebesgue differentiation theorem via the rising sun lemma |
scientific article; zbMATH DE number 2151959 |
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The Lebesgue differentiation theorem via the rising sun lemma (English)
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4 April 2005
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An elegant proof of Lebesgue's differentiation theorem is obtained using a version of the rising sun lemma for continuous functions and a reduction of the main statement to the continuous case, based on the fact that a strictly increasing function on an interval has a continuous inverse. Only basic properties of Lebesgue outer measure are needed, making this a suitable approach for an elementary course.
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Lebesgue differentiation theorem
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monotone function
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