Category:Definitions/Essentially Bounded Functions

This category contains definitions related to Essentially Bounded Functions.
Related results can be found in Category:Essentially Bounded Functions.

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

Let $f : X \to \R$ be a $\Sigma$-measurable function.

We say that $f$ is essentially bounded if and only if there exists a real number $c$ such that:

$\map \mu {\set {x \in X : \size {\map f x} > c} } = 0$