Let $X, Y \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number such that
Let $p \in [0, \infty)$ be an D4767: Unsigned real number such that
(i) | \begin{equation} X \overset{d}{=} Y \end{equation} |
(i) | \begin{equation} \mathbb{E} |X|^p < \infty \end{equation} |
Then
\begin{equation}
\mathbb{E} |X|^p
= \mathbb{E} |Y|^p
\end{equation}