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Results tagged with fa.functional-analysis
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user 97212
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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Separability of $L^1$ in $L^2$ topology
In the space $L^1(0,1)$ take the topology generated by the $L^2$-balls
$$B^2_r(f)=\{g\in L^1(0,1):\; \|f-g\|_2<r\}.$$
Is $L^1(0,1)$ separable in this topology?
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