ThmDex – An index of mathematical definitions, results, and conjectures.
F10657
Formulation 2
Let $M = (X, \mathcal{F}, \mu)$ be a D2707: Sigma-bounded measure space such that
(i) $f : X \to [0, \infty]$ is an D5610: Unsigned basic Borel function on $M$
Then \begin{equation} \int_X f \, d \mu = \int_{[0, \infty]} \mu(\{ x \in X : f(x) \geq t \}) \, d t \end{equation}