Formula_13125

\[\begin{gathered}\left(p \frac{1}{x}, \varphi\right)=\text { v.p. } \int \frac{\varphi(x)}{x} d x=\lim _{\varepsilon \rightarrow+0}\left\{\int_{-\infty}^{-\varepsilon}+\int_{+\varepsilon}^{+\infty} \frac{\varphi(x)}{x} d x\right\}, \\\left(\frac{1}{x+i 0}, \varphi\right)=\lim _{\varepsilon \rightarrow+0} \int \frac{\varphi(x)}{x+i 0} d x, \quad \varphi \in D\left(\mathbb{R}^{1}\right),\end{gathered}\]