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Jul
2
awarded  Curious
Aug
3
awarded  Yearling
Jul
9
accepted Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
Jul
9
comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
Thanks! Everything clear now.
Jul
9
comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
This is as a close to an answer as I can get, but before I accept it, one thing to clarify: this measure theory stuff is related to Lebesgue integration and the given integral can be shown, using Lebegue theory, to be convergent and its value is zero. Is that what are you are saying?
Jul
9
comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
@DonAntonio No was confused about the comment itself not my question. The comment was somewhat contradictory but N.S. cleared things. Anyway, I've edited the question to be clear about what I'm asking for. Different? Oh well, then I'll post a new question. thx!
Jul
9
revised Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
Cleared question
Jul
9
comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
@Omnomnomnom Yes you actually understood my question!! Thx. @ ZettaSuro : I assume you we responding to N.S. comment..
Jul
9
comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
@DonAntonio I do know it is not convergent and how to to show, was rather confused about what N.S. meant. My question is more like this: Riemann integration says this integral diverges. Does this mean Lebegue integration and other integration theories will behave the same with this integral? [Should probably put this in question].
Jul
9
comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
@N.S. no method can show this integral is convergent,...,since it is not convergent: how do you know it is not convergent if there is no method to show that? I'm a tad confused here. :-(
Jul
9
asked Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$
Feb
19
comment Verification of a proof involving Hausdorff max. principle and collections
@AsafKaragila Thanks for the patience and corrections!!!
Feb
19
revised Verification of a proof involving Hausdorff max. principle and collections
And so `S ` is monotone.
Feb
19
revised Verification of a proof involving Hausdorff max. principle and collections
Changed notation as not to imply index on sets are indexing sets
Feb
19
comment Verification of a proof involving Hausdorff max. principle and collections
@AsafKaragila The basics are never funny! :-) Thanks very much!!!
Feb
19
revised Verification of a proof involving Hausdorff max. principle and collections
deleted 90 characters in body
Feb
19
accepted Verification of a proof involving Hausdorff max. principle and collections
Feb
19
revised Verification of a proof involving Hausdorff max. principle and collections
deleted 4 characters in body
Feb
19
revised Verification of a proof involving Hausdorff max. principle and collections
added 4 characters in body
Feb
19
revised Verification of a proof involving Hausdorff max. principle and collections
Final proof for future readers as per answer enlightenment