ThmDex – An index of mathematical definitions, results, and conjectures.
Two random real numbers identical in distribution have identical absolute moments
Formulation 0
Let $X, Y \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number such that
(i) \begin{equation} X \overset{d}{=} Y \end{equation}
Let $p \in [0, \infty)$ be an D4767: Unsigned real number such that
(i) \begin{equation} \mathbb{E} |X|^p < \infty \end{equation}
Then \begin{equation} \mathbb{E} |X|^p = \mathbb{E} |Y|^p \end{equation}