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Lebesgue analysis

  1. May 2, 2008 #1
    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?

  2. jcsd
  3. May 2, 2008 #2


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    Homework Helper

    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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