ThmDex – An index of mathematical definitions, results, and conjectures.
F13494
Formulation 4
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) \begin{equation} \mu(X) < \infty \end{equation}
(ii) $f : X \to \mathbb{C}$ is a D5148: Borel-measurable complex function on $M$
(iii) $p, q \in [1, \infty]$ are each an D5237: Unsigned basic number
(iv) \begin{equation} p > q \end{equation}
(v) \begin{equation} \Vert f \Vert_p < \infty \end{equation}
Then \begin{equation} \Vert f \Vert_q < \infty \end{equation}