[分析] f(x,y) continuous

[GSXSP (Gloria)]

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.


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→ kerwinhui   : any condition on A?  E.g., false for A=R.
→ GSXSP       : Can you give me an example for A=R, thanks.
→ r19891011   : Int_{y \in R}exp(-ixy) dy=2 $pi $delta(x)
Add a constraint f(x,y) \in R, real function

→ willydp     : f(x,y)=(x/√π)exp(-y^2/x^2)
→ willydp     : x∈[-1, 1], y∈R
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