Let $(X,\mathcal{A},\mu)$ be a [measure space](/page/Measure%20Space), let $\mathbb{F}\in\{\mathbb{R},\mathbb{C}\}$ be the scalar field of the functions, and suppose that $\mu(X)<\infty$. Let $1 \leq p < q \leq \infty$. If $f \in L^q(X,\mathcal{A},\mu;\mathbb{F})$, then $f \in L^p(X,\mathcal{A},\mu;\mathbb{F})$, and