ThmDex – An index of mathematical definitions, results, and conjectures.
▼ 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
Definition D316
Set of P-integrable complex Borel functions
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $\mathcal{M} = \mathcal{M}(X \to \mathbb{C})$ is the D5578: Set of complex Borel functions on $M$
The set of P-integrable complex functions on $M$ with respect to $p \in [1, \infty)$ is the D11: Set \begin{equation} \mathfrak{L}^p(M \to \mathbb{C}) : = \left\{ f \in \mathcal{M} : \int_X |f|^p \, d \mu < \infty \right\} \end{equation}
Children
▶ D317: Lebesgue length function
▶ D3083: Set of P-integrable random complex numbers