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Could you please help me with the following? I think it is a Lebesgue Dominated Convergence Theorem but I am not sure.

Compute the following: For $1\leq p<\infty$ and $f\in L^p(\mathbb{R})$ $$\lim_{h\rightarrow \infty}\int_{-\infty}^\infty\left|f(x+h)-f(x)\right|^p \, dx$$

uranix
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user163644
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  • This is essentially the same as http://math.stackexchange.com/questions/1018716/translation-operator-and-continuity or http://math.stackexchange.com/questions/157397/proof-that-translation-of-a-function-converges-to-function-in-l1 . – PhoemueX Jul 29 '15 at 18:50
  • You shouldn't say "using LDCT" in the title unless the problem specifies you're supposed to use LDCT. In fact that doesn't help here... – David C. Ullrich Jul 29 '15 at 19:04
  • @ PhoemueX, Normal Human, Davide Giraudo I think the suggestion helps if the limit goes to 0 instead of infinity. – user163644 Jul 29 '15 at 21:46

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