s j+--si+' -- -s2

sj+1 s


 Figure 2-11 Partition of [(0,0),(s,t)]


=> If((,t) f(O,t i+)+ Rf If(si,ti) f(si,t 1 ). Putting


the two together we have, for each i


!f(si,ti) f(si3 1,ti+1)l


 = If(s ,ti) f(s ,ti+1) + f(siti+ ) f(s3i+l' t 1)l


 < If(si,t ) f(si,ti+ )l + If(sl,t+ ) f(si+iti+1)


 I AR. f R f + f f(si,0) f(si+ 10)I + Bf(O,t ) f(0,t)i+1
 1 1

Now, upon summing over the i's, we have