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About: Reduced derivative     Goto   Sponge   NotDistinct   Permalink

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In mathematics, the reduced derivative is a generalization of the notion of derivative that is well-suited to the study of functions of bounded variation. Although functions of bounded variation have derivatives in the sense of Radon measures, it is desirable to have a derivative that takes values in the same space as the functions themselves. Although the precise definition of the reduced derivative is quite involved, its key properties are quite easy to remember: * it is a multiple of the usual derivative wherever it exists; * at jump points, it is a multiple of the jump vector.