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9:50 AM
A new tag was created by Olivier Bégassat.
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Q: $s$-finite vs. $\sigma$-finite measures

Olivier BégassatMany results in measure theory are first proven for finite measures and then extended to $\sigma$-finite ones. Here are some examples: $\pi\text{-}\lambda$ theorem approach to proving two measures are the same. Fubini-Tonelli. Lebesgue decomposition. Radon-Nikodym theorem. Other results (e.g. D...

In mathematics, more precisely in measure theory, Lebesgue's decomposition theorem states that for every two σ-finite signed measures μ {\displaystyle \mu } and ν {\displaystyle \nu } on a measurable space ( Ω , Σ ) , {\displaystyle (\Omega ,\Sigma ),} there exist two σ-finite signed measures ν 0 {\displaystyle \nu _{0}} and...
 

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