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Can anyone help me to find the limit of the following problem ?

$$\lim_{r\to0^+} \frac{1}{2r} \int^{r+t}_{-r+t} h(x,y) dy $$

What i think here is to use lesbegue differentiation theorem. I am not being successful. Can anyone give me hints to solve it explicitly.

$h$ is continuous .

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    What are the hypothesis on $h$?2012-07-18
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    Is $h$ continuous in $y$ at $(x,t)$?2012-07-18
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    Did you mean to have $x$ as the limit variable or $r$?2012-07-18
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    @copper.hat : i have edited . sorry for typo.2012-07-18
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    What topology do you have on your function space? The limit will be a function of $x$, so it's important to specify what it means for a family of functions to converge. Are we looking at the $L^p$ norm? Pointwise convergence? Uniform convergence?2012-07-18
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    @Theorem : You need to specify for us the family of functions $h$. It would really help. Otherwise I don't think we can do much here in general.2012-07-18
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    @AlexBecker : I am particularly not assuming that it belongs to particular function space or a particular convergence . I would definitely appreciate if you point out for which function space does it actually make sense .2012-07-18

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