Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
Let $p \in (0, \infty)$ be a D993: Real number.
(i) | $f : X \to [0, \infty]$ is an D5610: Unsigned basic Borel function on $M$ |
Then
\begin{equation}
\Vert f \Vert_{L^p}^p
= \int^{\infty}_0 \mu (f > t) \, d t^p
\end{equation}