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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.
Jun
11
comment is there any one one and onto function from $A$ to $B$
You could start by writing down the sets $A$ and $B$ in simpler forms. They are both open intervals.
Jun
11
comment True if sigma-compact
What do we know about the topology of $X$?
Jun
11
revised Form of $\sigma(X_n)$ and $\sigma(X_n)$-measurability
added 1 characters in body
Jun
11
answered Form of $\sigma(X_n)$ and $\sigma(X_n)$-measurability
Jun
10
comment Evaluating $\int \frac{dx}{x^2 - 2x} dx$
@MarkBennet: The latter part to the answer was included after all the previous comments took place. And the first part, it is purely unnecessary steps to obtain $\frac{1}{x(x-2)}$ from $\frac{1}{x^{2}-2x}$.
Jun
10
comment Evaluating $\int \frac{dx}{x^2 - 2x} dx$
My intention is not to complain, if it seemed like that then I am glad I can correct the misunderstanding. I'm just having hard time seeing why this answer is useful. Do you really think that $x^{2}-2x=x(x-2)$ is what the OP is having hard time to figure out?
Jun
10
comment Evaluating $\int \frac{dx}{x^2 - 2x} dx$
You start from $\frac{1}{x^{2}-2x}$ and end up with $\frac{1}{x(x-2)}$ with 2 unnecessary middle-steps. You could just take $x$ as common multiplier in the first place.