Suppose { f n } {\displaystyle \{f_{n}\}} is a sequence of non-negative measurable functions, f n : X → [ 0 , + ∞ ] {\displaystyle f_{n}:X\to [0,+\infty ]} . Then: ∫ lim inf n → + ∞ f n ≤ lim inf n → + ∞ ∫ f n {\displaystyle \int \liminf _{n\rightarrow +\infty }f_{n}\leq \liminf _{n\rightarrow +\infty }\int f_{n}} . [1]
For any <math> n\in\mathbb{N} <math>
is a sequence of non-negative measurable functions, ![{\displaystyle f_{n}:X\to [0,+\infty ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c40303a8eaaeaa98d29ac2ac62dc40c14dd2f35)
.
Then:
. [1]