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.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I couldn't find it on Google. I know that $L^1_{\text{loc}}(\mathbb{R}^n) $ is the space of locally integrable functions, but what about $L^\infty_{\text{loc}}(\mathbb{R}^n) $?

Thanks a lot!

share|cite|improve this question
$f \in L^{\infty}_{\mathrm{loc}}(\mathbb{R}^n)$ if, for every compact set $K \subset \mathbb{R}^n$, $f \in L^{\infty}(K)$. – Christopher A. Wong Nov 21 '12 at 2:53
Thanks Christopher! – Peter Valk Nov 21 '12 at 3:02
up vote 1 down vote accepted

In general, $f\in L^p_{\text{loc}}(\mathbb{R}^n)$ if for every compact $K\subset\mathbb{R}^n$, $f\chi_K\in L^p(\mathbb{R}^n)$ where $\chi_K$ denotes the indicator function of $K$.

share|cite|improve this answer
Thank you very much icurays1! – Peter Valk Nov 21 '12 at 3:02
Note the minor edit - $f\vert_K$ didn't quite make sense in this context. – icurays1 Nov 21 '12 at 3:03

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.