According to Wikipedia: In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset.
Can you give me a simple real-world/common example/application of that, illustrating how each part of the definition is involved in the application/example?
I am trying to understand why Degrees (angle measurement) work. I think they are an example of measure, but I don't know how that is.
EDIT: I looked up the word "measure" (since degrees are measurements of angles), and that came to me.
In measuring rotations, we assign every amount of rotation a number, which would be the size of the rotation. It seemed similar to "a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset."