Category:Complex Measure-Integrable Functions

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

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

Let $\struct {\C, \map \BB \C}$ be the complex numbers made into a measurable space with its Borel $\sigma$-algebra.

Let $f : X \to \C$ be a $\Sigma/\map \BB C$-measurable function.

Let $\map \Re f : X \to \R$ and $\map \Im f : X \to \R$ be the real part and imaginary part of $f$ respectively.

We say that $f$ is $\mu$-integrable if and only if $\map \Re f$ and $\map \Im f$ are (real) $\mu$-integrable.