Set function

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In mathematics, a set function is a function whose input is a set. The output is usually a number. Often the input is a set of real numbers, a set of points in Euclidean space, or a set of points in some measure space.

Examples[edit]

Examples of set functions include:

  • The function that assigns to each set its cardinality, i.e. the number of members of the set, is a set function.
  • The function
 d(A) = \lim_{n\to\infty} \frac{|A \cap \{1,\dots,n\}|}{n},
assigning densities to sufficiently well-behaved subsets A ⊆ {1, 2, 3, ...}, is a set function.

References[edit]

  • A.N. Kolmogorov and S.V. Fomin (1975), Introductory Real Analysis, Dover. ISBN 0-486-61226-0

Further reading[edit]