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 Apr 26 awarded Yearling Oct 5 awarded Popular Question Aug 30 awarded Nice Answer Jul 22 awarded Notable Question Apr 26 awarded Yearling Dec 17 accepted A question about continuous functions Dec 17 asked A question about continuous functions Nov 15 comment Question about the Ascoli-Arzelá Theorem proof Why the fact that $\{f_n: n \in \mathbb{N}\} \subset H$ implies that $\{f_n: n \in \mathbb{N}\}$ is equicontinuous? Nov 15 asked Question about the Ascoli-Arzelá Theorem proof Nov 1 accepted Open Mappinig Theorem doubts on Brezis's Book Nov 1 comment Open Mappinig Theorem doubts on Brezis's Book I understand now thank you. Nov 1 comment Open Mappinig Theorem doubts on Brezis's Book Thank you very much, I only don't undertand what do you mean by "balanced"? Nov 1 asked Open Mappinig Theorem doubts on Brezis's Book Sep 30 awarded Explainer Sep 10 comment How are the essential upper and lower limits defined? But there $\operatorname*{ess\,sup} F(x) = inf\{ a : \mu(\{x:f(x)>a\}) =\emptyset$. Can I conclude $\operatorname*{ess\,sup} F(x) = inf\{a: \mu(0<|x-x^*|<0 : \{f>a\}) =\emptyset$? Sep 10 comment How are the essential upper and lower limits defined? I thank your answer. But, what does \$\operatorname*{ess\,sup}_{0<|x-x^*|