- #1
Bashyboy
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Homework Statement
I am working through a theorem on necessary and sufficient conditions for a set to be measurable and came across the following claim used in the proof: Let ##E## be measurable and ##m^*(E) = \infty##. Then ##E## can be written as a disjoint union of a countable collection of measurable sets, each of which have a finite outer measure.
Homework Equations
The Attempt at a Solution
I am not really sure where to begin. I have searched through my book and haven't found any theorem/lemma even remotely like this. Is this lemma used part of more general theorem? If so, what does that theorem look like? I did a google search and couldn't find anything.