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 Feb26 awarded Yearling Jul2 awarded Curious Jun10 comment Approximation of $C^\alpha(T^2)$ in $L^1$ by a $C^k$ function Yes. Here I want a $C^k$, $k<\infty$ approximation, also I want the approximation in $L^1$. Given these milder restrictions (as opposed to $C^\infty$ and approximation in $L^\infty$) I wonder what is the best bound one can get for $\|f_\epsilon\|_{C^k}$. Jun9 comment Approximation of $C^\alpha(T^2)$ in $L^1$ by a $C^k$ function Could you show me the calculation? Jun5 asked Approximation of $C^\alpha(T^2)$ in $L^1$ by a $C^k$ function Jul7 accepted The boundedness of $x^k e^{-|x|}$ Jul4 comment The boundedness of $x^k e^{-|x|}$ Thanks @Ethan . Jul4 asked The boundedness of $x^k e^{-|x|}$ Jul3 asked approximate Fourier transform May23 awarded Yearling May9 awarded Caucus Apr16 comment Bernoulli shift on $S^\mathbb{Z}$ First prove it for cylinders. Then prove it for finite unions of cylinders. I think then you can use an approximation argument: approximate (in symmetric difference) an arbitrary measurable set with finite union of cylinders. Apr16 comment Nonconstant linear functional on a topological vector space is an open mapping You are assuming $f$ is continuous, which is not part of Rudin's statement. Apr16 revised Nonconstant linear functional on a topological vector space is an open mapping added 21 characters in body Apr16 revised Nonconstant linear functional on a topological vector space is an open mapping Fixed some typos. Apr16 suggested approved edit on Nonconstant linear functional on a topological vector space is an open mapping Apr16 awarded Benefactor Apr15 revised Nonconstant linear functional on a topological vector space is an open mapping added 7 characters in body; edited title Apr13 accepted Weakest hypothesis for integration by parts Apr13 comment Weakest hypothesis for integration by parts Can you provide the proof of $G$ being absolutely continuous? Also what assumptions do you need to integrate the right side of equation (2)?