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How to proceed with the proof of the above theorem?

- Thread starter suvadip
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- Thread starter
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How to proceed with the proof of the above theorem?

- Feb 13, 2012

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If an f(x,y) is continous in a

How to proceed with the proof of the above theorem?

$\displaystyle G(y) = \int_{a}^{b} f(x,y)\ dx\ (1)$

... for any h>0 is...

$\displaystyle |G(y + h) - G(y)| = | \int_{a}^{b} \{ f(x,y+h) - f(x,y)\}\ dx| \le \int_{a}^{b} |f(x,y+h) - f(x,y)|\ d x\ (2)$

Now f(x,y) is uniformly continous so that choosing h 'small enough' You can do the last term of (2) 'small as You like' and that means that G(y) is continous...

Kind regards

$\chi$ $\sigma$