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Amir Sagiv
Amir Sagiv
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The characterization of norm compactness in $L^p$: you want the Frechét-Kolmogorov theorem, usually stated for $X=\mathbb{R}^n$ and $Y:=\mathbb{R}$. The proof follows quite easily formfrom Ascoli-Arzelà by mollification. You can find it on HaïmHaïm Brezis'  Functional Analysis.

The characterization of norm compactness in $L^p$: you want the Frechét-Kolmogorov theorem, usually stated for $X=\mathbb{R}^n$ and $Y:=\mathbb{R}$. The proof follows quite easily form Ascoli-Arzelà by mollification. You can find it on Haïm Brezis'  Functional Analysis.

The characterization of norm compactness in $L^p$: you want the Frechét-Kolmogorov theorem, usually stated for $X=\mathbb{R}^n$ and $Y:=\mathbb{R}$. The proof follows quite easily from Ascoli-Arzelà by mollification. You can find it on Haïm Brezis' Functional Analysis.

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Pietro Majer
Pietro Majer
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The characterization of norm compactness in $L^p$: you want the Frechét-Kolmogorov theorem, usually stated for $X=\mathbb{R}^n$ and $Y:=\mathbb{R}$. The proof follows quite easily form Ascoli-Arzelà by mollification. You can find it on Haïm Brezis' Functional Analysis.