 that $$\lim_{\varepsilon\downarrow 0}\operatorname*{ess\,sup}_{u\in (v,v+\varepsilon)} \left\|\int_0^s\left[(\nabla^\frac{H}{0}\psi_r)(u)-(\nabla^\frac{H}{0}\psi_r)(v)\right]\delta{R}_r^H\right\|_{\mathbb{D}^{0,0}} 