Let $\displaystyle \lambda,\mu$ be Borel measures on $\displaystyle I=[0,1]$ for x-axis and y-axis. Let $\displaystyle d=\{(x,y): x<y\}\subset I\times I$.

a)show $\displaystyle d$ is measurable on $\displaystyle I\times I$.

b)Evaluate $\displaystyle \int_I \int_I 1_d d\lambda d\mu$, $\displaystyle \int_I \int_I 1_d d\mu d\lambda$, and $\displaystyle \int_{I\times I} 1_d d(\lambda \times \mu)$.

i have no idea how to do this. any help would be appreciated.