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seen Sep 23 at 0:33

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 $\operatorname*{ess\,sup}_{0<|x-x^*|<r} F(x)$ mean? Would you mind give a reference?
Sep
9
revised How are the essential upper and lower limits defined?
edited body
Sep
9
comment How are the essential upper and lower limits defined?
Is related but it is different.
Sep
9
asked How are the essential upper and lower limits defined?
Sep
7
accepted BMO functions are $L^p$ Loc for all $1<p<\infty$
Sep
7
comment BMO functions are $L^p$ Loc for all $1<p<\infty$
After your ask, I thought, I do not know if this notation exist but, what I mean is $\sup \{ \|f\|_{L^p(K)}:K \subset \subset \Omega\}$.
Sep
7
reviewed Approve suggested edit on Solution of $\frac{dx}{dt}=-\frac{(\sigma+1)x}{\sigma x+1}$ in terms of Lambert $w$ function
Sep
7
reviewed Approve suggested edit on What is the general solution to $2n d^2+4= v^4$
Sep
7
revised BMO functions are $L^p$ Loc for all $1<p<\infty$
added 1 character in body
Sep
7
asked BMO functions are $L^p$ Loc for all $1<p<\infty$
Aug
12
revised Regularity of a a transmission problem
added 31 characters in body
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
25
accepted Regularity of a function between two paraboloids tangents
Jun
4
asked Change of variables to flatten the boundary
May
22
accepted Possible mistake in Safonov's lemma
May
14
asked Possible mistake in Safonov's lemma
May
3
comment Proof of the 'second' triangle inequality
Yes, your proof is right and I'm saying that one usual notation for the scalar product in $ \mathbb{R}^n$ is $\langle x, y \rangle $ you may also use $ x \cdot y$. If you do not do this people could think that you are proving the real case.
May
2
answered Proof of the 'second' triangle inequality