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!
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!
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 $K$.