Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
| (i) | $f_0, f_1, f_2, \cdots : X \to [0, \infty]$ are each an D5610: Unsigned basic Borel function on $M$ |
Then
| (1) | \begin{equation} \int_X \liminf_{n \to \infty} f_n \,d \mu \leq \liminf_{n \to \infty} \int_X f_n \,d \mu \end{equation} |
| (2) | \begin{equation} \int_X \limsup_{n \to \infty} f_n \,d \mu \geq \limsup_{n \to \infty} \int_X f_n \,d \mu \end{equation} |