[分析] 實變問題

看板Math作者 (YES)時間11年前 (2013/03/22 19:36), 編輯推噓3(301)
留言4則, 4人參與, 最新討論串1/3 (看更多)
想請教實變高手教我下面兩題實變題目: 1.Let f be integrable over [0,1]. Show that exp[∫f(x)dx ]< = ∫exp(f(x))dx. 2.Let g be a positive measurable function on [0,1]. Show that log(∫g(x)dx)> = ∫log (g(x))dx whenever each side is defined. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 124.11.174.172

03/22 20:22, , 1F
Jensen
03/22 20:22, 1F

03/22 23:02, , 2F
一個convex 一個concave
03/22 23:02, 2F

03/23 14:55, , 3F
凹凸有致
03/23 14:55, 3F

03/24 00:55, , 4F
謝謝提示!!了解了!
03/24 00:55, 4F
文章代碼(AID): #1HJ48loD (Math)
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文章代碼(AID): #1HJ48loD (Math)