ThmDex – An index of mathematical definitions, results, and conjectures.
Triangle inequality for signed basic expectation
Formulation 0
Let $X \in \text{Random} [-\infty, \infty]$ be a D4381: Random basic number such that
(i) \begin{equation} \mathbb{E} |X| < \infty \end{equation}
Then \begin{equation} \mathbb{E} X \leq |\mathbb{E} X| \leq \mathbb{E} |X| \end{equation}
Proofs
Proof 0
Let $X \in \text{Random} [-\infty, \infty]$ be a D4381: Random basic number such that
(i) \begin{equation} \mathbb{E} |X| < \infty \end{equation}
This result is a particular case of R2014: Triangle inequality for signed basic integral. $\square$