# Thread: R - S integrals of bounded function

1. ## R - S integrals of bounded function

Let α be of bounded variation on [a,b]. let V(n) be the total variation of α on [a,x] and let V(a)=0 . if f Є R(α), prove that f Є R(V)?Let α be of bounded variation on [a,b]. let V(n) be the total variation of α on [a,x] and let V(a)=0 . if f Є R(α), prove that f Є R(V)?

Now how do i show that U(P,f,V) - L(P,f,V) < ε, and how does the info V(a) = 0 help here?

thanx

2. ## Re: R - S integrals of bounded function

Sorry, what is $R(V)$?

3. ## Re: R - S integrals of bounded function

R(V) means that a function is reimann integrable. Like f is reimann integrable on alpha

4. ## Re: R - S integrals of bounded function

Is there anyone who can help me with this?

Thanx