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.
In formal notation, we can make any set into a measurable space by taking the sigma-algebra of measurable subsets to consist of all subsets of . Then the counting measure on this measurable space is the positive measure defined by
- Schilling, René L. (2005)."Measures, Integral and Martingales". Cambridge University Press.
- Hansen, Ernst (2009)."Measure theory, Fourth Edition". Department of Mathematical Science, University of Copenhagen.