generated from smyalygames/quartz
503 B
503 B
Definition
Have Measure \mu on X, and f_{n} : X \to [0, \infty] Measurable. Then \int \lim_{ n \to \infty } \inf f_{n} \, d\mu \le \lim_{ n \to \infty } \inf \int f_{n} \, d\mu
[!info] What is
\lim\inf? Definition of Infimum (it is basically the opposite of a Supremum).
\{ x_{n} \} \subset [0, \infty]\lim_{ n \to \infty }\inf x_{n} = \sup_{m}\inf_{n \geq m} x_{n}
\inf_{n \geq m} = y_{m} \leq y_{m+1} \leq \dots