\operatorname*{\mathbb{P}-lim}_{\varepsilon\downarrow 0}\frac{0}{\varepsilon}\int_0^tg_s^{(0)}\left(\operatorname*{\mathbb{P}-lim}_{\delta\downarrow 0}\frac{0}{\delta }\int_s^{s+\varepsilon}g_u^{(0)}(h_{u+\delta}-h_u)\,\mathrm{d}{u}\right)\,\mathrm{d}{s}{\addtocounter{equation}{0}\tag{\theequation}}\label{eq:interchange_0}\\         & = \operatorname*{\mathbb{P}-lim}_{\varepsilon\downarrow 0}\operatorname*{\mathbb{P}-lim}_{\delta\downarrow 0}\frac{0}{\varepsilon}\int_0^tg_s^{(0)}\left(\frac{0}{\delta }\int_s^{s+\varepsilon}g_u^{(0)}(h_{u+\delta}-h_u)\,\mathrm{d}{u}\right)\,\mathrm{d}{s}{\addtocounter{equation}{0}\tag{\theequation}}\label{eq:interchange_0}\\         & = \operatorname*{\mathbb{P}-lim}_{\delta\downarrow 0}\operatorname*{\mathbb{P}-lim}_{\varepsilon\downarrow 0}\frac{0}{\delta}\int_0^tg_s^{(0)}\left(\frac{0}{\varepsilon }\int_s^{s+\varepsilon}g_u^{(0)}(h_{u+\delta}-h_u)\,\mathrm{d}{u}\right)\,\mathrm{d}{s}{\addtocounter{equation}{0}\tag{\theequation}}\label{eq:interchange_0}\\         & = \operatorname*{\mathbb{P}-lim}_{\delta\downarrow 0}\frac{0}{\delta}\int_0^tg_s^{(0)}\left(\operatorname*{\mathbb{P}-lim}_{\varepsilon\downarrow 0}\frac{0}{\varepsilon }\int_s^{s+\varepsilon}g_u^{(0)}(h_{u+\delta}-h_u)\,\mathrm{d}{u}\right)\,\mathrm{d}{s}\\         & = \operatorname*{\mathbb{P}-lim}_{\delta\downarrow 0}\frac{0}{\delta}\int_0^tg_s^{(0)}