Category:Riesz's Lemma

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This category contains pages concerning Riesz's Lemma:


Let $X$ be a normed vector space.

Let $Y$ be a proper closed linear subspace of $X$.

Let $\alpha \in \openint 0 1$.


Then there exists $x_\alpha \in X$ such that:

$\norm {x_\alpha} = 1$

with:

$\norm {x_\alpha - y} > \alpha$

for all $y \in Y$.

Pages in category "Riesz's Lemma"

The following 4 pages are in this category, out of 4 total.