ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Simple map
Simple function
Measurable simple complex function
Simple integral
Unsigned basic integral
P-integrable basic function
Set of P-integrable complex Borel functions
Lebesgue length function
Complex Lebesgue quotient set
Definition D3189
Complex random Lebesgue quotient set
Formulation 0
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) \begin{equation} {\sim} : = \left\{ (X, Y) \in \mathfrak{L}^p \times \mathfrak{L}^p : \Vert X - Y \Vert_{\mathfrak{L}^p} = 0 \right\} \end{equation}
The complex random Lebesgue quotient set on $P$ with respect to $p$ is the D180: Quotient set \begin{equation} \mathfrak{L}^p / {\sim} \end{equation}