ABSTRACT
It follows that F is increasing and incrementally increasing. F is also right continuous on R × L. In fact, let , (t,x) R × L, and (tn ,xn) a sequence in R × L with tn t and xn x, with tn t and xn x. For each n let t'n , x'n Q be such that tn < t'n < tn + 1
n and xn < x'n +
1 n
. Then t'n t,t'n > t and x'n x, x'n > x. If N, then
F( , t, x) = lim G( , t'n, x'n) ¿From
F( , t, x) F( , t'n, x'n) < G( , t'n, x'n)
we deduce that lim F( , tn, xn) = F( , t, x); hence F is right continuous at (t, x). If N, F is also, evidently, right continuous.
