[分析] 一題實變L^p問題

[BA0954016 (YES)]

Assume that E has finite measure and 1<=p1<p2<=∞. Show that if {fn}→f in
L^p2(E),then {fn}→f in L^p1(E).

想請問高手可否給我一些解題方向!感謝!

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推 zhanguihan  :by Holder inequlity
→ BA0954016   :那要怎麼用這個inequality證明?可以再多說明一點嗎><
推 mitmosfet   :先寫下∫(|fn-f|^p1) 然後回想一下Holder inquality
→ mitmosfet   :的敘述
推 mitmosfet   :我打錯了 是inequality
→ BA0954016   :那對應到Holder inequality中的g要如何設定?
→ mitmosfet   :設g=1就行了
→ BA0954016   :OK!我大概知道怎麼做了!