[分析] f(x,y) continuous

看板Math作者 (Gloria)時間11年前 (2014/11/01 04:31), 11年前編輯推噓0(0推 0噓 5→)
留言5則, 4人參與, 最新討論串1/2 (看更多)
Prove or disprove that If f(x,y) bounded and continuous in (x,y), then Int_{y \in A } f(x,y) dy is continuous in x. -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 166.170.48.149 ※ 文章網址: http://www.ptt.cc/bbs/Math/M.1414787482.A.40C.html
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11/01 07:45, , 1F
any condition on A? E.g., false for A=R.
11/01 07:45, 1F
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11/01 08:12, , 2F
Can you give me an example for A=R, thanks.
11/01 08:12, 2F
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11/02 02:12, , 3F
Int_{y \in R}exp(-ixy) dy=2 $pi $delta(x)
11/02 02:12, 3F
Add a constraint f(x,y) \in R, real function
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11/02 07:10, , 4F
f(x,y)=(x/√π)exp(-y^2/x^2)
11/02 07:10, 4F
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11/02 07:12, , 5F
x∈[-1, 1], y∈R
11/02 07:12, 5F
int_{y\in R} (x/√π)exp(-y^2/x^2) dy = x^2 is continuous did I miss something? ※ 編輯: GSXSP (132.239.223.126), 11/06/2014 02:00:51
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文章代碼(AID): #1KK_6QGC (Math)
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文章代碼(AID): #1KK_6QGC (Math)