# Problem related to signed measure

1. Dec 3, 2008

### onthetopo

1. The problem statement, all variables and given/known data
(X,S,u) a measure space and f is in L1.
Show that for any e>0, there exists a set E with u(E)<+infinity such that
$$| \int_{E} fdu - \int_{X} fdu |<e$$

3. The attempt at a solution
we can define a function
$$v(A)=\int_{A}fdu$$
It is a well known result that v(A) is in fact a signed measure.

We can somehow use the property of signed measures to show that there always exist a E such that |v(E)-v(X)|<e?

2. Dec 3, 2008

### morphism

Don't you need sigma-finiteness here or something of the sort?

3. Dec 5, 2008

### onthetopo

The question is as is, there is no mention of sigma finiteness. My attempt at the solution could be completely wrong.

4. Dec 5, 2008

### grossgermany

Let's suppose it is sigma finite? then what?