Can Lebesgue Analysis Exchange Sums of Finite Terms?

[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

 

[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