→ kkk3388 :你看看這樣對不對???? 04/18 22:29
※ 引述《BA0954016 (YES)》之銘言：
: 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!
S {|fn-f|xE}^p1 dx
|| (fn-f)X_E ||p1 < ||fn-f||p2 ||X_E||r
since E has finite measure , ||X_E||r be a constant. QED
X_E(x)=1 for x belong to E ,otherwise be zero.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.39.45.238