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Definition D117
Complex Lebesgue quotient set

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) $${\sim} : = \left\{ (f, g) \in \mathfrak{L}^p \times \mathfrak{L}^p : \Vert f - g \Vert_{\mathfrak{L}^p} = 0 \right\}$$
The complex Lebesgue quotient set on $M$ with respect to $p$ is the D180: Quotient set $$\mathfrak{L}^p / {\sim}$$
Children
 ▶ D3189: Complex random Lebesgue quotient set