(Sn't) (s,t) (s',t)









 (sntn) (s',tn




 Figure 3-5 Approximation of a horizontal interval


 Again, we have


 mf(J) = lim m (Rn
 n

 lim (f(s',t) f(s',t ) f(s ,t) + f(s ,t ))
 n n n n

 = f(s',t) f(ss,t_) f(s_,t+) + f(s_,t_).


With these in hand, we can compute the measure of the half-open and

open intervals: We write I{s x (t,t'] = I \ C(s,t)}, so


mf(Is}x(t,t']) = mf(I) mf(I(s,t)})


 f(s,t') f(s_,t;) f(s ,t_) + f(s_,t_) (f(s,t)