Convexity and symmetric derivatives of measurable functions (Q802774)
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scientific article; zbMATH DE number 4198362
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convexity and symmetric derivatives of measurable functions |
scientific article; zbMATH DE number 4198362 |
Statements
Convexity and symmetric derivatives of measurable functions (English)
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1991
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The author denotes by \(D+C\) the class of functions which can be obtained as the sum of a Darboux and a continuous function. The main result of the paper asserts: If \(f\in D+C\) is measurable on an open interval I and if the second lower symmetric derivate of f is nonnegative on I, then f is convex on I. This result is a solution of a problem raised by C. E. Weil.
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Darboux function
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measurable function
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convexity
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continuous function
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symmetric derivate
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0.8153854012489319
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0.7974487543106079
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0.7738955020904541
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0.7606222629547119
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