ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D3189
Complex random Lebesgue quotient set

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) $${\sim} : = \left\{ (X, Y) \in \mathfrak{L}^p \times \mathfrak{L}^p : \Vert X - Y \Vert_{\mathfrak{L}^p} = 0 \right\}$$
The complex random Lebesgue quotient set on $P$ with respect to $p$ is the D180: Quotient set $$\mathfrak{L}^p / {\sim}$$