Hi all,

I have the following questions:

1. Suppose $\displaystyle f : [0, \infty ) \mapsto R$ is bounded, concave and nondecreasing. Does it follow that f is continuous on $\displaystyle [0, \infty)$?

2. Suppose $\displaystyle f_{n} : [0, \infty ) \mapsto R $ are bounded, concave , continuous and nondecreasing. Let f be the pointwise limit of $\displaystyle f_{n}$, does it follow that f is continuous?