ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Simple map
Simple function
Measurable simple complex function
Simple integral
Unsigned basic integral
P-integrable basic function
Set of P-integrable complex Borel functions
Definition D3083
Set of P-integrable random complex numbers
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $\mathcal{M} = \mathcal{M}(\Omega \to \mathbb{C})$ is the D5584: Set of random complex numbers on $M$
The set of P-integrable random complex numbers on $P$ with respect to $p \in [1, \infty)$ is the D11: Set \begin{equation} \mathfrak{L}^p(P \to \mathbb{C}) : = \left\{ Z \in \mathcal{M} : \mathbb{E} |Z|^p < \infty \right\} \end{equation}
Set of P-integrable random basic real numbers