Young's Inequality for Convolutions/Corollary 2

Corollary to Young's Inequality for Convolutions
Let $f, g: \R^n \to \R$ be Lebesgue integrable functions.

Then their convolution $f * g$ is also Lebesgue integrable and $\Vert f*g\Vert \leq \Vert f \Vert \Vert g \Vert$. Thus, convolution may be seen as a binary operation $*: \mathcal{L}^1 \times \mathcal{L}^1 \to \mathcal{L}^1$ on the space of integrable functions $\mathcal{L}^1$.

Proof
Apply Young's Inequality for Convolutions with $p =q = r = 1$.