Can Lebesgue Analysis Exchange Sums of Finite Terms?

  • Thread starter natski
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  • #1
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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
 
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  • #2
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
 

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