Counting measure

In mathematics, the counting measure is an intuitive way to put a measure on any set: the "size" of a subset is taken to be the number of elements in the subset, if the subset has finitely many elements, and ∞ if the subset is infinite.

The counting measure can be defined on any measurable set, but is mostly used on countable sets.

In formal notation, we can make any set X into a measurable space by taking the sigma-algebra ${\displaystyle \Sigma }$ of measurable subsets to consist of all subsets of ${\displaystyle X}$. Then the counting measure ${\displaystyle \mu }$ on this measurable space ${\displaystyle (X,\Sigma )}$ is the positive measure ${\displaystyle \Sigma \rightarrow [0,+\infty ]}$ defined by

...
Wikipedia