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 Yearling
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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