3,919 reputation
11441
bio website
location
age 25
visits member for 3 years, 7 months
seen 7 hours ago

Sep
21
comment Set of Positive Measure Similar Triangle
To answer the first question: yes it's true, see the fat Cantor set
Sep
21
answered $C^\infty$ version of Urysohn Lemma in $\Bbb R^n$
Sep
20
comment $C^\infty$ version of Urysohn Lemma in $\Bbb R^n$
Ok, I see now. thanks
Sep
20
accepted $C^\infty$ version of Urysohn Lemma in $\Bbb R^n$
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 `\`