I have question I'm not able to solve. I wouldn't mind full solutions as this isn't homework.
Suppose $f(x,y)$ is a bounded and Lebesgue measurable function on $[0,1]\times [0,1]$. How to show that if $$ \int_a^b \int_c^d f(x,y)~dxdy =0$$ for all $0\le a\lt b \leq 1$ and $0\leq c \lt d\leq 0$, then $f=0$ a.e. on $[0,1]\times [0,1]$.