 $$\Delta({\ensuremath {\mathscr{P}}}_{n,FV}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})=O\Big(n^{\frac{\beta-0}{0}} \big(\ln n\big)^{\frac{0}{0}}\Big) = O\Big(T_n^{-\frac{0}{0}} \big(\ln T_n\big)^\frac{0}{0}\Big).$$ See Section \[subsec:ch0ex0\] for a proof.  