Integral of Increasing Function Composed with Measurable Function/Corollary

Corollary to Integral of Increasing Function Composed with Measurable Function
Let $\struct {X, \Sigma, \mu}$ be a measure space.

Let $p \in \R$ such that $p \ge 1$. Let $f: X \to \R$ be a $p$-integrable function.

Then:


 * $\ds \norm f_p^p = \int_0^\infty p t^{p - 1} \map F t \rd t$

where $F$ is the survival function of $\size f$.