Limiting weak-type behavior for singular integral and maximal operators

The following limit result holds for the weak-type (1,1) constant of dilation-commuting singular integral operator $T$ in $\mathbb{R}^n$: for $f\in L^1(\mathbb{R}^n)$, $f\geq 0$,

$\lim_{\lambda\rightarrow 0} \lambda\hspace{1mm}m\{x\in\mathbb{R}^... ...a\} = \frac{1}{n} \int_{S^{n-1}}\vert\Omega(x)\vert d\sigma(x)\Vert f\Vert _1.$

For the maximal operator $M$, the corresponding result is

$\lim_{\lambda\rightarrow 0} \lambda\hspace{1mm}m\{x\in\mathbb{R}^n: \vert Mf(x)\vert>\lambda\} = \Vert f\Vert _1.$