Rudin Reference

1. Oct 7, 2008

Nusc

Hello,

I was wondering where I can find a proof to the following theorem:

If F is differentiable at every pt. of [a,b] and if F' is lebesque on [a,b] then

F(x) = int(f,dt,a,x) a<=x<=b.

And the converse.

He gives the theorem are page 324 and a reference in his bibliography. I was wondering where I detailed proof for this theorem.

2. Oct 7, 2008

morphism

He proves that in his Real & Complex Analysis book. It's Theorem 8.21 on page 169 of the first edition.

3. Oct 7, 2008

Nusc

Thank you dearly.

4. Oct 8, 2008

Nusc

Hey morphism,

do you know where I can find the proofs for the theorems 11.23 (a), (d), (e), (f), 11.24(b), 11.26, 11.27, 11.29, and 11.32 extended to Lebesgue integrals of complex functions?

5. Oct 9, 2008

morphism

Have you tried to prove them yourself? They easily follow from their real-valued analogues.

6. Nov 14, 2008

Nusc

He just gives the converse to

If F is differentiable at every pt. of [a,b] and if F' is lebesque on [a,b] then

F(x) = int(f,dt,a,x) a<=x<=b.

Where can I find the proof for this?

7. Nov 14, 2008

Nusc

Sorry, the actual theorem is:

If f in L on [a,b] and F(x)=int(f,t,a,x) (a<=x<=b) then F'(x)=f(x) almost everywhere on [a,b].

and he uses strictly eveywhere for continuity, why is this>

8. Nov 15, 2008

morphism

I'm not sure that I understand what it is you're asking.

Like I said, this is in one of his other books (with your typos corrected!), Real and Complex Analysis.

Where is this from? And continuity of what is being used?

9. Nov 15, 2008

Nusc

It was from baby rudin on page 324. I can only find the proof for the converse in Real and Complex Analysis.