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In mathematics, Ehrling's lemma is a result concerning Banach spaces. It is often used in functional analysis to demonstrate the equivalence of certain norms on Sobolev spaces. It was proposed by Gunnar Ehrling. ==Statement of the lemma== Let (''X'', ||·||''X''), (''Y'', ||·||''Y'') and (''Z'', ||·||''Z'') be three Banach spaces. Assume that: * ''X'' is compactly embedded in ''Y'': i.e. ''X'' ⊆ ''Y'' and every ||·||''X''-bounded sequence in ''X'' has a subsequence that is ||·||''Y''-convergent; and * ''Y'' is continuously embedded in ''Z'': i.e. ''Y'' ⊆ ''Z'' and there is a constant ''k'' so that ||''y''||''Z'' ≤ ''k''||''y''||''Y'' for every ''y'' ∈ ''Y''. Then, for every ''ε'' > 0, there exists a constant ''C''(''ε'') such that, for all ''x'' ∈ ''X'', : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ehrling's lemma」の詳細全文を読む スポンサード リンク
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