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Possible Duplicate:
On distributions over $\mathbb R$ whose derivatives vanishes

Why can I identify a distribution $G \in \mathcal{D}'((a,b))$, $\partial G = 0$ by a constant function?

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Hint: fix a test function $\psi_0$ of integral $1$ and for $\phi\in \mathcal D((a,b))$, put $f(x):=\int_a^x\phi(t)dt-\int_a^b\phi(t)dt\int_a^x\psi_0(t)dt.$ Check that $f$ is a test function, and compute $f'$. Then compute $G(f')$ to get the wanted result.

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    @JayeshBadwaik Yes, it is a typo.2015-06-02