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Sep
20
comment $C^\infty$ version of Urysohn Lemma in $\Bbb R^n$
I just found what I've asked is just the Section 2.6 "Constructions of Smooth Functions" of the book Differentiable Manifolds by Lawrence Conlon. What do you mean by "Note that the entire cube is within $\frac{\Delta}{2}.$"
Sep
19
comment Riemann Sum Approximation
It depends of the specific $f$. And if $f$ is integrable, for any positive number you can find an $n$ so that the error is bounded by that number.
Sep
19
comment What is the inverse function of $\ x^2+x$?
+1 for good title.
Sep
19
revised $C^\infty$ version of Urysohn Lemma in $\Bbb R^n$
edited body
Sep
18
revised $C^\infty$ version of Urysohn Lemma in $\Bbb R^n$
added 944 characters in body
Sep
18
asked $C^\infty$ version of Urysohn Lemma in $\Bbb R^n$
Sep
17
comment Proving Thomae's function is nowhere differentiable.
@PeterTamaroff yes I was following those lines of thought
Sep
17
comment Proving Thomae's function is nowhere differentiable.
Well it is a good exercise, just let flow the definitions of limit of a function and limit of a sequence.
Sep
17
comment Proving Thomae's function is nowhere differentiable.
Without the hint: 1. Recall that another equivalent definition of differentiability of $f$ at $a$ is _$f$ is diff. at $a$ iff $$\displaystyle{\lim_{x\to a} \frac{f(x)-f(a)}{x-a}}\in\Bbb R$$._ 2. Use the fact that for any function $h$, $\lim_{x\to a}h(x)=l$ iff for each sequence $(x_n)$ with $x_n\to a$, $\lim_{n\to\infty}f(x_n)=l$.
Sep
15
comment Lebesgue measure and matrix notation problem
Is this your book?
Sep
13
comment Question Related to Theorem that “Union of Two Measurable Sets is Measurable”
You can answer your own question :-) (to remove this from the list of unanswered questions).
Sep
11
revised $L_p$ norm not subadditive for $0<p<1$ when endowed on $C[0,1]$
TeX
Sep
7
revised If $E$ has measure zero, then does $E^2$ have measure zero?
Improving the title and adding a relevant definition
Sep
7
revised Maps from sets of measure zero to sets of measure zero
TeX things
Sep
5
revised system of open intervals
added 108 characters in body
Sep
5
revised system of open intervals
Some missing `\`
Sep
5
answered system of open intervals
Aug
29
comment If $A$ and $B$ are compact, then so is $A+B$.
related Jonas Meyer answer
Aug
28
comment Is it true that if $B$ is compact then $\operatorname{Cl}(A+B)=\operatorname{Cl}(A)+\operatorname{Cl}(B)$?
related
Aug
26
comment Morse functions are dense in $\mathcal{C}^\infty(X,\mathbb{R})$.
You can answer your own question so that the post is useful to someone else.