- #1

polkadot66

- 1

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- Homework Statement
- Given ## f \in L^1(X, M, \mu)## , show there is a ## \sigma## -finite measure ## \mu'## such that ## \int_{E} f d\mu = \int_{E} f d\mu'## .

- Relevant Equations
- ## f \in L^1## so ## \int |f| d\mu < \infty##

a measure ## \mu'## is ## \sigma##-finite if there are sets ##A_1, A_2, ...## such that ## \mu'(A_n) < \infty## and ##X= \cup A_n##

I tried to prove this by absurd stating that there is no such ## \mu'## but i couldn't get anywhere...