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 Mar 29 awarded Yearling Mar 29 accepted A reference for an inequality Mar 29 asked A reference for an inequality Feb 15 comment How to prove $\int_{-\infty}^{+\infty}|f(x+t) - f(x)|dx \to 0$ as $t\to 0$ @DavidC.Ullrich, FYI I found a hint in the book. The way to go is to approximate $f$ using step functions. Feb 13 comment How to prove $\int_{-\infty}^{+\infty}|f(x+t) - f(x)|dx \to 0$ as $t\to 0$ @DavidC.Ullrich, It is the very first example in the book. The author shows that we can approximate $f$ with a smooth function convolution, exactly as you mention. But in the end of the proof, they use the fact I asked question about. Feb 13 comment How to prove $\int_{-\infty}^{+\infty}|f(x+t) - f(x)|dx \to 0$ as $t\to 0$ @DavidC.Ullrich, the book is Smoothing and Approximation of Functions by Harold Shapiro Feb 12 revised How to prove $\int_{-\infty}^{+\infty}|f(x+t) - f(x)|dx \to 0$ as $t\to 0$ added 6 characters in body; edited title Feb 12 comment How to prove $\int_{-\infty}^{+\infty}|f(x+t) - f(x)|dx \to 0$ as $t\to 0$ Thank you, that is my mistake that I thought that the Donimated theorem is the tool to go. I am going to edit the question. Feb 12 comment How to prove $\int_{-\infty}^{+\infty}|f(x+t) - f(x)|dx \to 0$ as $t\to 0$ This what I actually need to prove :-). I need to prove this results that we can approximate $f$ with a continuous function. And In the proof, this is the last step. Feb 12 comment How to prove $\int_{-\infty}^{+\infty}|f(x+t) - f(x)|dx \to 0$ as $t\to 0$ $f$ is not necessary continuous. What type of approximations do we need in the general case? Feb 12 asked How to prove $\int_{-\infty}^{+\infty}|f(x+t) - f(x)|dx \to 0$ as $t\to 0$ Dec 23 accepted Build a DAG with minimal number of nodes with no incoming edges. Dec 21 asked Build a DAG with minimal number of nodes with no incoming edges. Nov 16 accepted Examples of $C^1$ differentiable convex functions. Nov 16 asked Examples of $C^1$ differentiable convex functions. Aug 28 accepted Barrier cone of a convex set. Why it is a cone? Aug 28 comment Barrier cone of a convex set. Why it is a cone? Thank you for the explanation. I thought that $\beta$ should be the same for all $x^*$. Is it correct that a barrier cone for a bounded convex set is whole $\mathbb{R}^n$? Aug 27 asked Barrier cone of a convex set. Why it is a cone? May 28 awarded Notable Question Apr 26 awarded Popular Question