# Prove increasing function defines everywhere is Rinemann-integrable

1. Nov 25, 2007

### quasar987

1. The problem statement, all variables and given/known data
This is probably easy but i cant 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.

3. The attempt at a solution

2. Nov 25, 2007

### 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.

3. Nov 25, 2007

### 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)

4. Nov 25, 2007

### CompuChip

It will work. Try it