Liminf of Indicator Sequence is Indicator of Liminf

Last updated Nov 1, 2022

Let $({A}{n}){n=1}^{\infty} \subset X$ be a Sequence of Sets. Then $$\liminf\limits_{n \to \infty} \mathbb{1}{A{n}} = \mathbb{1}{\liminf\limits{n \to \infty} A_{n}}.$$

TODO similar to Limsup of Indicator Sequence is Indicator of Limsup

• Indicator Function
• Liminf of a Set Sequence
• Liminf of Sequence