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 $M$

The Lebesgue distance function on $\mathfrak{L}^p$ is the D4367: Unsigned real function \begin{equation} \mathfrak{L}^p \times \mathfrak{L}^p \to [0, \infty), \quad (f, g) \mapsto \left( \int_X |f - g|^p \, d \mu \right)^{1 / p} \end{equation}