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Measure, wikipedia article


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."

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    measured in metric kickasses.2012-02-27

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In measure theory, it is perhaps better to think of the measure of a set as a generalization of length if you're working on the real line, (or as area or volume in higher dimensional settings). Measure theory doesn't really have anything to do with degree measure. One of the main uses of measure theory is in integration.