Rudy the Reindeer
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 Mar 24 comment Real analysis: collection of sets - sigma-algebra or not? @DidierPiau Yes you're right. Thanks for the downvote. Mar 24 answered Real analysis: collection of sets - sigma-algebra or not? Mar 24 comment $\varphi$ in $\operatorname{Hom}{(S^1, S^1)}$ are of the form $z^n$ Plus one. I can't verify your answer because I don't know enough about lie groups. But I'm grateful that someone posted an alternative proof. Mar 24 comment $\varphi$ in $\operatorname{Hom}{(S^1, S^1)}$ are of the form $z^n$ I see. Thanks! And thanks for your answer! Mar 24 answered $\varphi$ in $\operatorname{Hom}{(S^1, S^1)}$ are of the form $z^n$ Mar 23 comment Countability of boundary points Oh I see. It's vocabulary from the question. Mar 23 comment Countability of boundary points What is a strictly open interval? Mar 23 comment $\varphi$ in $\operatorname{Hom}{(S^1, S^1)}$ are of the form $z^n$ I don't understand your explanation why $\int_0^a g(t) dt$ can't be zero. Could you elaborate? Thanks! Mar 23 comment $\varphi$ in $\operatorname{Hom}{(S^1, S^1)}$ are of the form $z^n$ @ZhenLin Heh. "...we need a couple of lemmas..." -- I thought this proof was going to be a one liner. Thanks for the link. So that's one way of proving this. Mar 23 asked $\varphi$ in $\operatorname{Hom}{(S^1, S^1)}$ are of the form $z^n$ Mar 22 revised Orthogonality relations of Characters Tags edited. Mar 22 comment Question on Lipschitz condition. Can't you use that if $f$ is absolutely continuous then it's differentiable almost everywhere and then apply the fundamental theorem of calculus? Mar 22 comment Orthogonality relations of Characters @rk101 Glad I could help : ) Mar 22 revised Orthogonality relations of Characters Explanation added in response to comment. Mar 22 comment Orthogonality relations of Characters @rk101 Yes, that's right, the bar corresponds to complex conjugation. In this case conjugation corresponds to taking inverses. I've added the explanation in the answer. Hope this helps. Otherwise don't hesitate to ask. Mar 22 revised Orthogonality relations of Characters added 26 characters in body Mar 22 answered Orthogonality relations of Characters Mar 20 revised About product measure and Tonelli-Fubini Theorem: Show that H is closed under increasing limit and differences. Typo corrected. Mar 20 revised uniformly continuous functions in [0,∞) Tags edited. Mar 20 comment uniformly continuous functions in [0,∞) @t.b. Nice, thank you for providing the missing parts to my answer. : )