ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Simple map
Simple function
Measurable simple complex function
Simple integral
Unsigned basic integral
Unsigned basic expectation
Basic expectation
Random real number moment
Definition D2014
Random real number absolute moment
Formulation 1
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) $p \in (0, \infty)$ is a D5407: Positive real number
(ii) \begin{equation} \mathbb{E} |X|^p < \infty \end{equation}
The absolute moment of $X$ with respect to $p$ is the D993: Real number \begin{equation} \mathbb{E} |X|^p \end{equation}
Results
R4126: Almost surely bounded random complex number has all absolute moments finite