ThmDex – An index of mathematical definitions, results, and conjectures.
F13492
Formulation 2
Let $Z \in \text{Random}(\mathbb{C})$ be a D4877: Random complex number such that
(i) $p, q \in [1, \infty)$ are each a D5407: Positive real number
(ii) \begin{equation} p > q \end{equation}
(iii) \begin{equation} \mathbb{E} |Z|^p \in [0, \infty) \end{equation}
Then \begin{equation} \mathbb{E} |Z|^q \in [0, \infty) \end{equation}