Fubini in $\mathbb{R^2}$

Question

$\lambda:\mathcal{B}(\mathbb{R^2})\to [0,\infty]$

$A:=${$x\in\mathbb{R^2}:x_1+x_2\leq1$}$\subseteq\mathbb{R^2}$

$B:=${$x\in\mathbb{R^2:x_1,x_2}\geq0$}$\subseteq\mathbb{R^2}$

So I have to show $\int_{B}\mathbb{1}_Ad\lambda$. And $1$ should be the characteristic funktion. And I know I am allowed to use Fubini. But I am not sure how to start. Could someone give me help for the beginning? Thanks

Answer 1

You can start with $\int_B 1_A d\lambda = \int_{\mathbb{R}^{2}} 1_{A\cap B} d\lambda = \lambda(A\cap B)$.