One way to define usc (lsc):

A function f is upper semicontinuous at a point x_0 if either f(x_0)=\infty or for each M > f(x_0), there is a positive \delta such that if |x-x_0| < \delta, then M > f(x). f is lower semicontinous at x_0 if -f is upper semicontinuous at x_0.