# What is “approximation in a Sobolev Space”? For example,

I want to know the meaning of the statement as below.

$$\text{There is a sequence} \;\{f_k\} \subset W^{3,2}\; \text{approximating}\;\; f \;\;\text{in}\;\; W^{2,2}.$$

Here $W^{n,m}$ means a Sobolev Space.

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Presumably this means that each $f_k$ is in $W^{3,2}$ and $f_k \rightarrow f$ in the norm of $W^{2,2}$ (i.e. $\|f_k - f\|_{W^{2,2}} \rightarrow 0$.) – user15464 May 26 '12 at 20:23
@user15464 Thank you very much. – Misaj May 26 '12 at 20:27
@user15464 You could post your comment as an answer. – Davide Giraudo May 27 '12 at 9:38

## 1 Answer

Presumably this means that each $f_k$ is in $W^{3,2}$ and $f_k\rightarrow f$ in the norm of $W^{2,2}$ (i.e. $\|f_k-f\|_{W^{2.2}}\rightarrow 0$).

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