# fubini's theorem

• Dec 22nd 2009, 01:52 PM
Kat-M
fubini's theorem
show the function $f(x,y)=\frac{x^2-y^2}{(x^2+y^2)^2}$ is not Lebesgue integrable on (0,1)X(0,1).

Apply Fubini's theorem and use $\frac{x^2-y^2}{(x^2+y^2)^2}=\frac{1}{x^2+y^2} + \frac{y(-2y)}{(x^2+y^2)^2}$ and $\frac{d}{dy}\frac{1}{x^2+y^2}=\frac{-2y}{(x^2+y^2)^2}$

i have been stuck on this for a while. help me please.
• Dec 22nd 2009, 02:26 PM
Kat-M
fubini theorem
when i computed the integral $\int \int \frac{x^2-y^2}{(x^2+y^2)^2} dy dx$, i got $- \infty$. does it mean it is not lebesgue integrable. i do not know in general what i have to show to say it is not lebesgue integral. im grateful for any help please.
• Dec 22nd 2009, 02:36 PM
galactus
See here:

Fubini's theorem - Wikipedia, the free encyclopedia

They address this exact problem when explaining Fubini's theorem.