Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that

(i)	$\mathfrak{L}^p = \mathfrak{L}^p (M \to \mathbb{C})$ is a D316: Set of P-integrable complex Borel functions on $M$
(ii)	$\Vert \cdot \Vert_{\mathfrak{L}^p}$ is the D317: Lebesgue length function on $\mathfrak{L}^p$
(iii)	$$\begin{equation} {\sim} : = \left\{ (f, g) \in \mathfrak{L}^p \times \mathfrak{L}^p : \Vert f - g \Vert_{\mathfrak{L}^p} = 0 \right\} \end{equation}$$

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