Definition:Cauchy Principal Value/Real Integral

Definition
Let $f: \R \to \R$ be a real function which is piecewise continuous everywhere.

Then the Cauchy Principal Value of $\displaystyle \int f$ is defined as:


 * $\PV_{-\infty}^{+\infty} \map f t \rd t := \lim_{R \mathop \to +\infty} \int_{-R}^R \map f t \rd t$

where $\displaystyle \int_{-R}^R \map f t \rd t$ is a Riemann integral.