Prove increasing function defines everywhere is Rinemann-integrable

[quasar987]

Homework Statement

This is probably easy but i can't seem to see how to make it work right now.

I am trying to show that if we have a function f:R-->R that is increasing, then for any interval [a,b], it is riemann-integrable.

I know it's true because a book I saw refers to another book for the proof that an increasing fct as a countable number of discontinuities.

The Attempt at a Solution

 

[ZioX]

If you know the proof of the fact that f is Riemann integrable iff it is continuous (lambda) almost everywhere then try to work it in...countable sets have 0 measure, of course.

Ie, suppose f is discontinuous on some non-null set and derive a contradiction.

 

[quasar987]

Is this just an idea you're throwing at me, or do you know for a fact that it works?

(As a matter of fact, I have proven that very theorem in an earlier homework sheet for this course)

 

[CompuChip]

It will work. Try it