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I want to show that $\phi\mapsto\underset{\varepsilon\searrow 0}{lim}\int_{-\infty}^{\infty}\frac{\phi(x)}{x+i\varepsilon}dx$ defines a distribution on $\mathcal{D}(\mathbb{R})$ but I just don't come up with a good idea to show that. Second part would be to determine the order of it. Thanks for any suggestions.

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    Do you understand the arguments in this http://math.stackexchange.com/questions/162931/principal-value-as-distribution-written-as-integral-over-singularity recent question?2012-06-28

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