▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Simple map
▾ Simple function
▾ Measurable simple complex function
▾ Simple integral
▾ Unsigned basic integral
▾ P-integrable basic function
▾ Set of P-integrable complex Borel functions
▾ Set of P-integrable random complex numbers
Set of P-integrable random basic real numbers
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $\mathcal{M} = \mathcal{M}(\Omega \to \mathbb{R})$ is the D5586: Set of random basic real numbers on $M$
The set of P-integrable random basic real numbers on $P$ with respect to $p \in [1, \infty)$ is the D11: Set \begin{equation} \mathfrak{L}^p(P \to \mathbb{R}) : = \left\{ X \in \mathcal{M} : \mathbb{E} |X|^p < \infty \right\} \end{equation}