# Lebesgue integration

1. Jun 26, 2010

### wayneckm

Hello all,

I would like to know when the Lebesgue integration w.r.t. a right-continuous function, there would be a series part which takes account of the jump components.

Is it true that we require the series to be absolutely convergent? if so, what is the rationale of defining this instead of simply convergent?

Thanks very much.

Last edited: Jun 26, 2010
2. Jun 26, 2010

### mathman

The question is confusing (series part???). Could you give an example of what you are asking about.

3. Jun 26, 2010

### Hurkyl

Staff Emeritus
I think... he's talking about the Stieltjes-Lebesgue measure df(x)?

4. Jun 26, 2010

### wayneckm

Yup, it should be Lebesgue-Stieltjes integral $$\int f(x) d g(x)$$ with $$g(x)$$ being right-continuous.