measure

Measure

A measure is a set function $\mu$ that assigns a non-negative size or volume to subsets of a given set, generalizing concepts like length, area, volume, probability, … it tells you how much “stuff” is in a set.

$$\mu :\mathcal{F}\to [0,\infty ]$$

with $\mu (\varnothing )=0$, and countable additivity.