Definition:Survival Function

Definition
Let $\left({X, \Sigma, \mu}\right)$ be a measure space.

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

The cumulative distribution function of $f$ is the mapping $F \left({f}\right): \R \to \R$ defined by:


 * $\forall t \in \R: F \left({f}\right) \left({t}\right) := \mu \left({\left\{{f > t}\right\}}\right)$

where $\left\{{f > t}\right\}$ is the set $\left\{{x \in X: f \left({x}\right) > t}\right\}$.

Also known as
Some sources refer to this as a distribution function, but it can then become confused with the concept of a distribution function in physics.