Talk:Pointwise Lower Limit of Measurable Functions is Measurable
It turns out that the term Definition:Lower Limit is used in the context of topological spaces Definition:Lower Limit (Topological Space), and so the recommendation is that the term Definition:Limit Inferior be used instead.
(Of course, it may also be the case (it probably is) that Definition:Lower Limit (Topological Space) is also called a "limit inferior" so the disambiguation would need to be more subtle.)
But in any case, as we have been using Definition:Limit Inferior throughout, it is probably also a good idea to use the term Definition:Pointwise Limit Inferior instead of Definition:Pointwise Lower Limit.
- If you look at it, the lower limit as defined for topological spaces is actually employing the same construction as a lower limit of sets. Except it's more general than using just a sequence. I would take into account that we should always say "the lower limit of $f$ at $x_0$" or "the lower limit of $(x_n)_n$", or "the lower limit of $(A_n)_n$". So the chances of confusing things are not astronomical. So perhaps not everything has to be changed. — Lord_Farin (talk) 15:51, 9 June 2015 (UTC)