- #1
ECmathstudent
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Homework Statement
If a function f is of bounded variation on [a,b], show it is Riemann integrable
Homework Equations
Have proven f to be bounded
S(P) is the suprenum of the set of Riemann integrals of a partition (Let's say J)
s(P) is the infinum of J
S(P) - s(P) < e implies f is Riemann integrable
The Attempt at a Solution
I know I'm supposed to set up two partitions, one regular one and one so that for each second piece of the partition:
f(a i) >= Mi - c
f(a i+1) =< mi -c
This will give a new sum, and I'm supposed to use this to show that S(P) - s(P) is less than epsilon. Sorry I don't know how to use Latex!