- #1
mathmari
Gold Member
MHB
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Hey!
In $\mathbb{R}^d$ with the Lebesgue measure if $f \in L^p, 1 \leq p < +\infty$, and if for each $y$ we set $f_y(x)=f(x+y)$ then:
Could you give me some hints how to show that?? (Wondering)
In $\mathbb{R}^d$ with the Lebesgue measure if $f \in L^p, 1 \leq p < +\infty$, and if for each $y$ we set $f_y(x)=f(x+y)$ then:
- $f_y \in L^p$ and $||f||_p=||f_y||_p$
- $\lim_{y \rightarrow 0} ||f-f_y||_p=0$
Could you give me some hints how to show that?? (Wondering)