TITLE: What is the intuition behind signed measures?
QUESTION [5 upvotes]: I have a rather basic question, and I cannot really find an answer around.

What is the intuition behind the introduction of signed measures?

I am not referring to the mathematical properties of these objects. Rather, the problem is to get what we capture with them (concrete examples, etc).  
Any feedback is most welcome.
Thank you for your time.

REPLY [4 votes]: One example comes from physics: distance vs. displacement.
Distilling this to a signed measure would be like standing in front of an building layout poster with a "You Are Here" marker.  If you go right in the hallway, that's a positive displacement; if you go left, that's a negative displacement.
But taking the distance from the marker is positive, regardless of whether you go left or right.
If you were to take an expected value of the displacement of each room in the hallway from the point, it would be close to zero if you were near the center.  But the (unsigned) distance would be about $1/4$ of the length of the hallway.
Does this help a bit?