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



Maury Barbato
Posts:
792
From:
University Federico II of Naples
Registered:
3/15/05


Re: Graph of a Function
Posted:
Sep 15, 2011 4:10 PM


> 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



