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
Formulation 0
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 $M$
The Lebesgue length function on $\mathfrak{L}^p$ is the D4367: Unsigned real function \begin{equation} \mathfrak{L}^p \to [0, \infty), \quad f \mapsto \left( \int_X |f|^p \, d \mu \right)^{1 / p} \end{equation}
Also known as
Lebesgue seminorm
Child definitions
» D117: Complex Lebesgue quotient set
» D5594: Lebesgue distance function