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I'm currently trying to teach myself some measure theory and I'm stuck on trying to show the following:

Let [tex](X,M,\mu)[/tex] be a finite positive measure space such that [tex]\mu({x})>0[/tex] [tex]\forall x \in X[/tex] . Set [tex]d(A,B) = \mu(A \Delta B)[/tex], [tex]A,B \in X[/tex]. Prove that [tex]d(A,B) \leq d(A,C) + d(C,B)[/tex] .

Could someone perhaps help me on the way? I've tried various approaches (mostly "brute force" with different re-writings of both sides of the inequality) but every time there is some term left that doesn't quite fit. Feels like it's actually quite easy and that I'm just missing the point.

Thanks in advance, oh and btw if this does not come out in the correct tex format, how do I achieve that? My first time here

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# Measure theory and the symmetric difference

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