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Topic: Graph of a Function
Replies: 1   Last Post: Sep 15, 2011 4:10 PM

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Maury Barbato

Posts: 791
From: University Federico II of Naples
Registered: 3/15/05
Re: Graph of a Function
Posted: Sep 15, 2011 4:10 PM
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> Hello,
> does someone know an example of an injective function
>
> f:[0,1]->R such that the graph
>
> G={(x,y) in R^2 | y=f(x)}
>
> is not Lebesgue measurable in R^2?
>
> Thank you very very much fro your help.
> My Best Regards,
> Maury Barbato


Finally I found thta such a function can easily be
contructed using a set with strange properties defined
by Sierpinski. See Bogachev, Measure Theory, Vol. 2,
p. 232, Exercies 3.10.49.

My Best Regards,
Maury Barbato



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