Let $A,B \subseteq \mathbb R^d$ lebesgue measurable with finite Lebesgue measure and $f=\chi_A*\chi_B$
Show that $\|f\|_{L^\infty}\leq \min\{\lambda(A),\lambda(B)\}$
I know that $\|f\|_\infty\leq \sqrt{\lambda(A)}\sqrt{\lambda(B)}$ but this does not lead to the goal. Thanks for any hints.