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▾ P-integrable basic function
▾ Set of P-integrable complex Borel functions
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}
Child definitions
» D5585: Set of P-integrable random basic real numbers