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Answer by ottone for Class of Riemann integrable functions with antiderivative
Just a modest proposal so a comment (but I am not entitled). Every Riemann (even Lebesgue) integrable function, say on the line, can be regarded in a natural way as a distribution (the distributional...
View ArticleAnswer by Gro-Tsen for Class of Riemann integrable functions with antiderivative
A classical and simple example is given by the function $x \mapsto \sin\frac{1}{x}$ extended by $0\mapsto 0$, on (say) $[-1,1]$:It is discontinuous at $0$.It is a derivative (= has an antiderivative)...
View ArticleClass of Riemann integrable functions with antiderivative
We know that continuous functionsare Riemann integrable andhave an antiderivative.For each bounded function $f$ on an interval $[a, b]$, the Lebesgue integrability theorem guarantees that such an $f$...
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