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Links. I think the sentence I modified was incorrect; but an expert should know for sure. |
my previous remark was wrong. But there is no need to say "norm continuous". The concept of continuity is unambiguous here, it is continuous as a map between two normed spaces. |
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:<math> f \mapsto f(x) </math>
from ''H'' to the complex numbers is continuous for any ''x'' in ''X''. By the [[Riesz representation theorem]], this implies that there exists an element ''K''<sub>''x''</sub> of ''H'' such that for every function ''f'' in the space,
:<math> f(x) = \langle K_x, f \rangle. </math>
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