(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} |