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Jun
13
comment Vitali set of outer-measure exactly $1$.
@AsafKaragila: Thanks. Do you have some references for this where I could possibly look it up?
Jun
13
comment Vitali set of outer-measure exactly $1$.
@GiuseppeVitali: Do you know if anyone has gone through the details of this construction and checked whether it works and gives the desired set?
Jun
12
comment Collection of converging sequences determines the topology?
No problem. There is still one $X$ left though :-)
Jun
12
comment Collection of converging sequences determines the topology?
@BrianM.Scott: You define $\tau_{2}$ by using the notion of $X$ and $D$ simultaneously. That is the reason why I'm asking.
Jun
12
comment Collection of converging sequences determines the topology?
What role does $X$ play in the above construction. Is $D\subset X$?
Jun
12
revised Collection of converging sequences determines the topology?
added TeX.
Jun
12
suggested approved edit on Collection of converging sequences determines the topology?
Jun
12
comment Vitali set of outer-measure exactly $1$.
The person who down-voted is welcome to leave a comment and explain why so.
Jun
12
asked Vitali set of outer-measure exactly $1$.
Jun
12
revised Interior, exterior and boundary of sets in $\mathbb R^2$
added 10 characters in body
Jun
12
comment Interior, exterior and boundary of sets in $\mathbb R^2$
Your answer on $B$ is not correct.
Jun
12
answered Interior, exterior and boundary of sets in $\mathbb R^2$
Jun
12
comment Limits of Subsequences
With the same idea it actually follows that for any subsequence of $\{t_{n}\}$ we find such a subsequence of $\{s_{n}\}$ that decreases more rapidly. And I don't think we needed the fact that $s_{n}\leq t_{n}$ at all.
Jun
12
comment subsets probability question
What have you tried so far? And is this a homework?
Jun
11
comment True if sigma-compact
@SamL.: Thank you.
Jun
11
answered True if sigma-compact
Jun
11
comment Form of $\sigma(X_n)$ and $\sigma(X_n)$-measurability
@Justin: Topology is just the family of open sets. If it confuses you, you can ignore that part and simply think of $\mathscr{B}(X)$ being the Borel $\sigma$-algebra of $X$ the way you have it defined.
Jun
11
comment True if sigma-compact
Found it now. And it's true that this is very questionable since no proof is given. If $X$ is $\sigma$-compact then the Lemma is true, as $E$ is a countable union of Borel sets. Let me see if I'm able to do something with the locally compact Hausdorff case.
Jun
11
comment True if sigma-compact
I couldn't find this Lemma from Royden's book. What page is it?
Jun
11
comment is there any one one and onto function from $A$ to $B$
That is correct.