Let $D=D([0,1], \mathbb{R})$ be the space of cadlag functions $x$ with $x(0)=0$ and $x$ is continuous on $1$. If we endow $D$ with Skorokhod Metric, see:
http://en.wikipedia.org/wiki/C%C3%A0dl%C3%A0g
for definition. Then I would like to know whether the following functions are uniformly continuous w.r.t. Skorokhod Metric:
$$\pi(x):=x(1/2)$$
$$S(x)=\sup_{0\le t\le 1}x(t)$$
$$L(x)=\int_0^1x(t)dt$$
I didn't find an answer in Convergence of Probability Measures, if someone knows the result please let me know. Thanks a lot!