3,839 reputation
11440
bio website
location
age 25
visits member for 3 years, 6 months
seen 3 mins ago

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.
Aug
25
revised Measure of the boundary of an open set of finite measure
TeXting R^2; added 5 characters in body
Aug
23
comment Sequence of $C^1[0,1]$ functions $(f_n) \to f$ but $f \notin C^1[0,1]$
Usually differentiable on $[0,1]$ means differentiable in each point of $[0,1]$, except possibly in the endpoints where one can consider right and left derivatives. So, a function is not differentiable in $[0,1]$ if there is a point in $[0,1]$ where differentiability fails.
Aug
21
comment Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
@Broseph are you fully satisfied? It's all clear?
Aug
21
revised Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
Again, trying to improve the formatting
Aug
21
comment Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
You're right, it's a singleton, a singleton have outer measure zero so it is measurable. In the other hand, if you can proof that an open set is measurable by the third bullet of What you know it follows that a countable intersection of measurable sets is always measurable.
Aug
21
comment Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
If you can prove that open sets are measurable then that's a corolary. Do you can?
Aug
18
revised Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
deleted 20 characters in body
Aug
18
comment Vitali's theorem?
This might be useful
Aug
18
answered Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
Aug
18
revised Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
Trying to improve how the post looks.
Aug
18
comment Why is the Vitali set not necessarily equal to the interval e.g. [0,1]?
See here for detailed explanations of the construction of Vitali set(s).
Aug
18
comment Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
That's the proof I have in mind. They are equivalent so you can prove your assertion by proving Cratheodory "from scratch". I suggested that way in order to get some inspiration to proceed the way you want. Let me write something. Perhaps I come back with an answer in while.
Aug
17
comment Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
I agree with Nate's comment.
Aug
17
comment Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
Notice that Caratheodory Criterion is equivalent to the problem you pose. You can get a proof of the Caratheodory Criterion for example from the Wheeden & Zygmund's Measure and Integral book, to get some inspiration.
Aug
17
comment Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.
Perhaps useful
Aug
17
revised Proving sets are measurable
deleted 2 characters in body
Aug
15
revised Proving sets are measurable
deleted 1 characters in body