Definition:Essentially Bounded Function

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

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

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


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

Also see

 * Definition:Lebesgue Infinity-Space