Set-Input Function

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A Set-Input Function is a function whose function domain is from a Set Space.



References

2013


  • http://en.wikipedia.org/wiki/Set_function#Examples
    • 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: [math]\displaystyle{ d(A) = \lim_{n\to\infty} \frac{|A \cap \{1,\dots,n\}|}{n}, }[/math] assigning densities to sufficiently well-behaved subsets A ⊆ {1, 2, 3, ...}, is a set function.
      • The Lebesgue measure is a set function that assigns a non-negative real number to each set of real numbers. (Kolmogorov and Fomin 1975)
      • A probability measure assigns a probability to each set in a σ-algebra. Specifically, the probability of the empty set is zero and the probability of the sample space is 1, with other sets given probabilities between 0 and 1.
      • A possibility measure assigns a number between zero and one to each set in the powerset of some given set. See Possibility theory.

2006