Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I would like to prove that for a LSC function, its epigraph is closed. I saw some longer proof here, but why would the following not hold ? :

$f LSC := \liminf f(x_n) \ge f(x)$ when $x_n \rightarrow x$

then $x_n,a_n \rightarrow x,a \implies f(x) \le \liminf f(x_n) \le \liminf a_n = a$

so $x,a \in epi(f)$

share|improve this question
add comment

1 Answer

up vote 0 down vote accepted

This is a streamlined version of the proof in wikipedia. Perhaps it's a bit too streamlined (write it up using quantifiers!). Otherwise it appears perfectly valid to me.

share|improve this answer
yeah, i spotted other weird stuff in the article in reference. not to be taken as a reference ! –  nicolas Dec 31 '12 at 17:44
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.