Something went seriously wrong with my last post, everything just became a blur. The expressions aren't even in the correct places. Oh well, I'll fix it when I get home. morphism, thanks for pointing out that way to complete the proof. I still can't let go of the thought of rewriting the...
Now forgive me if I'm wrong, but doesn't x \in A \Delta B imply that x is in either A or B, but x \notin A \cap B ?
From drawing a Venn diagram for A \Delta C \cup C \Delta B I believe that this relation can be written (A \cup B \cup C) \ (A \cap B \cap C) . If this is correct...
Actually no, but I think I see where you're getting at. If I can prove this, it would imply that \mu(A \Delta B) \leq \mu((A \Delta C) \cup (C \Delta B)) .
Now I tried to prove the relation you mentioned, but I can't seem to do it. The expression for the A \Delta C \cup C \Delta B is to...
Hi,
I'm currently trying to teach myself some measure theory and I'm stuck on trying to show the following:
Let (X,M,\mu) be a finite positive measure space such that \mu({x})>0 \forall x \in X . Set d(A,B) = \mu(A \Delta B), A,B \in X. Prove that d(A,B) \leq d(A,C) + d(C,B) .
Could...