Category:Integrals of Measure-Integrable Functions

This category contains results about Integrals of Measure-Integrable Functions.
Definitions specific to this category can be found in Definitions/Integrals of Measure-Integrable Functions.

Let $\struct {X, \Sigma, \mu}$ be a measure space.

Let $f: X \to \overline \R$, $f \in \map {\LL^1} \mu$ be a $\mu$-integrable function.

Then the $\mu$-integral of $f$ is defined by:

$\ds \int f \rd \mu := \int f^+ \rd \mu - \int f^- \rd \mu$

where $f^+$ and $f^-$ are the positive and negative parts of $f$, respectively.