ThmDex – An index of mathematical definitions, results, and conjectures.
Result R3581 on D1719: Expectation
Absolute moment inherits finiteness from greater exponents for random complex number
Formulation 1
Let $Z \in \text{Random}(\mathbb{C})$ be a D4877: Random complex number such that
(i) $1 \leq q < p < \infty$ are each a D5407: Positive real number
(i) \begin{equation} \mathbb{E} |Z|^p < \infty \end{equation}
Then \begin{equation} \mathbb{E} |Z|^q < \infty \end{equation}