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

(i)	$\mathfrak{L}^p = \mathfrak{L}^p (P \to \mathbb{C})$ is a D3083: Set of P-integrable random complex numbers on $M$
(ii)	$\Vert \cdot \Vert_{\mathfrak{L}^p}$ is the D317: Lebesgue length function on $\mathfrak{L}^p$
(iii)	\begin{equation} {\sim} : = \left\{ (X, Y) \in \mathfrak{L}^p \times \mathfrak{L}^p : \Vert X - Y \Vert_{\mathfrak{L}^p} = 0 \right\} \end{equation}

The complex random Lebesgue quotient set on $P$ with respect to $p$ is the D180: Quotient set \begin{equation} \mathfrak{L}^p / {\sim} \end{equation}