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set_limes_inferior [2013/06/22 17:20] nikolaj created |
set_limes_inferior [2014/10/25 19:13] nikolaj |
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===== Set limes inferior ===== | ===== Set limes inferior ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $A\in \text{Seq}(X)$ | | + | | @#55CCEE: context | @#55CCEE: $A\in \text{Seq}(X)$ | |
- | + | | @#FF9944: definition | @#FF9944: $\underset{n\to\infty}{\liminf}A_n\equiv{\bigcap_{n=1}^\infty}\left({\bigcup_{k=n}^\infty}A_n\right)$ | | |
- | | @#55EE55: $\underset{n\to\infty}{\liminf}A_n$ | | + | |
- | + | ||
- | | @#55EE55: ${\bigcap_{n=1}^\infty}\left({\bigcup_{k=n}^\infty}A_n\right)$ | | + | |
==== Ramifications ==== | ==== Ramifications ==== | ||
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For a more possibly more elucidating explaination, see my answer in this Math.Se thread [[http://math.stackexchange.com/questions/107931/lim-sup-and-lim-inf-of-sequence-of-sets/412395#412395|this Math.SE thread]] | For a more possibly more elucidating explaination, see my answer in this Math.Se thread [[http://math.stackexchange.com/questions/107931/lim-sup-and-lim-inf-of-sequence-of-sets/412395#412395|this Math.SE thread]] | ||
- | ==== Context ==== | + | ==== Parents ==== |
Parameterized set | Parameterized set | ||
=== Parameter refinement of === | === Parameter refinement of === | ||
[[Sequence intersection]] | [[Sequence intersection]] | ||
- | === Parents === | + | === Related === |
[[Sequence union]] | [[Sequence union]] |