下列命题中正确的是
$\text{A.}$ 若 $\lim _{x \rightarrow x_0} f(x) \geqslant \lim _{x \rightarrow x_0} g(x) \Rightarrow \exists \delta>0$, 当 $0 < \left|x-x_0\right| < \delta$ 时 $f(x) \geqslant g(x)$.
$\text{B.}$ 若 $\exists \delta>0$ 使得当 $0 < \left|x-x_0\right| < \delta$ 时有 $f(x)>g(x)$ 且 $\lim _{x \rightarrow x_0} f(x)=A_0, \lim _{x \rightarrow x_0} g(x)=B_0$ 均 $\exists$, 则 $A_0>B_0$.
$\text{C.}$ 若 $\exists \delta>0$, 当 $0 < \left|x-x_0\right| < \delta$ 时 $f(x)>g(x) \Rightarrow \lim _{x \rightarrow x_0} f(x) \geqslant \lim _{x \rightarrow x_0} g(x)$.
$\text{D.}$ 若 $\lim _{x \rightarrow x_0} f(x)>\lim _{x \rightarrow x_0} g(x) \Rightarrow \exists \delta>0$, 当 $0 < \left|x-x_0\right| < \delta$ 时有 $f(x)>g(x)$.