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visits member for 2 years, 4 months
seen Feb 9 '13 at 12:37

Jan
16
comment What is your definition for neighborhood in topology?
Would you please answer my comment above?
Jan
16
comment What is your definition for neighborhood in topology?
@Zhen I'm completely unfamiliar with the definition in wikipedia. Does the existence of a neighborhood (wikipedia definition) of $x$ gurantees the the existence of a open set containing $x$ then?
Jan
16
accepted What is your definition for neighborhood in topology?
Jan
16
asked What is your definition for neighborhood in topology?
Jan
15
comment What is wrong in my proof? (Uniform convergence and Lebesgue integral)
I want to make it clear. Is "$f$ is Lebesgue Integrable" same as saying "$f\in L^1(\mu)$"?
Jan
15
accepted What is wrong in my proof? (Uniform convergence and Lebesgue integral)
Jan
15
comment What is wrong in my proof? (Uniform convergence and Lebesgue integral)
@Ilya Now i got it thank you!
Jan
15
comment What is wrong in my proof? (Uniform convergence and Lebesgue integral)
@Ilya Oh right.. So the fake part is the last part. That is, [$|\int_X f_n-f d\mu|=0 \text{ implies } \int_X f_n d\mu - \int_X f d\mu =0$] is false, since it might me $\infty-\infty$. Am I right?
Jan
15
asked What is wrong in my proof? (Uniform convergence and Lebesgue integral)
Jan
15
accepted Is there an abbreviation for “almost all $x\in X$”?
Jan
15
asked Is there an abbreviation for “almost all $x\in X$”?
Jan
14
comment Why does measure have to be complete in this sentence?
@Learner Thank you!
Jan
14
accepted Why does measure have to be complete in this sentence?
Jan
14
comment Why does measure have to be complete in this sentence?
I didn't know you wrote an answer so i just added the question 3. Sorry for that..
Jan
14
revised Why does measure have to be complete in this sentence?
added 315 characters in body; edited tags
Jan
14
asked Why does measure have to be complete in this sentence?
Jan
14
comment Does the existence proof of $\mu$-completion require choice?
@Asaf I got it. Thank you for helping me.
Jan
14
comment Does the existence proof of $\mu$-completion require choice?
@Asaf How can i prove that $\mathfrak{M}^*$ is a $\sigma$-algebra without choice? Would you please write that as an answer?
Jan
14
comment Does the existence proof of $\mu$-completion require choice?
@Asaf Yes. I want to show that $\mathfrak{M}^*$ is a $\sigma$-algebra. So far, I have shown that $X\in\mathfrak{M}^*$ and [$E\in\mathfrak{M}^*\Rightarrow X\setminus E\in\mathfrak{M}^*$]
Jan
14
comment Does the existence proof of $\mu$-completion require choice?
@Asaf only if it is true, but it seems false now. My main interest is whether there exists a $\mu$-completion in ZF :)