# Lebesgue analysis

1. May 2, 2008

### natski

Hi all,

I'm aware that in Lebesgue analysis, one can interchange between the sum of infinite terms of an integral to the integral of a sum of infinite terms,... but what about a sum of finite terms? If the sum goes to N rather than infinity, can a sum inside an integral still be taken outside?

Natski

2. May 2, 2008

### lurflurf

That is even easier.
-integrals are linear
-no need to consider convergence
-you could write the finite sum as an infinite sum with only a finite number of nonzero terms