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Homework Statement
Suppose that S and T are sets with outer content 0, prove that SUT also has outer content zero.
Homework Equations
C(S) denotes the outer content.
C(S) = C(T) = 0
Also : [itex]C(S) = inf \left\{{ \sum_{k=0}^{n} A_k}\right\}[/itex] where Ak is the area of one of the sub-rectangles Rk.
The Attempt at a Solution
So we want to show that C(SUT) = 0 using the fact C(S) = C(T) = 0. I'm not really sure where to start this one though. First time I've seen anything like it and a quick search yielded no results about outer content at all.
I do have one theorem though. If S is a curve of finite length L, then C(S) = 0. I also figured ( not positive about this ) that C(∅) = 0.
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