Talk:Limit superior and limit inferior

From Wikipedia, the free encyclopedia

You have new messages (last change).

here is a problem with this definiton: For isolated points of the domain of the function (closure points for the domain of the function, but not limit points) the inferior and superior limits of the function exists while the limit doesn't exist (since the limit is defined only on limit points of the domain). For example, f(x)=x, E=[0,1]\cup{2}, f:E->R. The inferior and superior limits at x=2 both exists and both have value 2 while the limit of the function at x=2 is not defined.

Surely the example you give does have limit 2 at x=2, since in any sufficiently small neighbourhod of x=2, the function has value 2?

[edit] Should we have sigma algebras and lattices here?

I have a small concern about the section on sequences of sets: since we can define lim sup and lim inf of sequences of sets without ever mentioning sigma algebras and complete lattices, do we really need to mention them here? Just a bit concerned that someone coming here to find out about lim sup of sets might be a bit put off by these extra concepts. Madmath789 18:30, 13 October 2006 (UTC)

Retrieved from "http://en.wikipedia.org../../../l/i/m/Talk%7ELimit_superior_and_limit_inferior_20b7.html"