Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$\mathcal{M} = \mathcal{M}(\Omega \to \mathbb{R})$ is the D5586: Set of random basic real numbers on $M$

The set of P-integrable random basic real numbers on $P$ with respect to $p \in [1, \infty)$ is the D11: Set $$\begin{equation} \mathfrak{L}^p(P \to \mathbb{R}) : = \left\{ X \in \mathcal{M} : \mathbb{E} |X|^p < \infty \right\} \end{equation}$$