I'm doing an exercise from baby Rudin (chapter 8 exercise 11) and found a suggestion that it might use.
$$\left|\int_0^\infty e^{-x}f\left(\frac{x}{t}\right)dx\ -1\right| \leq \int_0^\infty e^{-x}\left|f\left(\frac{x}{t}\right) -1\right|dx$$
However, I don't quite understand what rule or theorem makes this possible. I think it might have something to do with the integral of $e^{-x}$ from 0 to infinity being 1 but am not sure. Does anyone have insight or suggestions as to what I might investigate to get my head around it?