Set function

Examples

• The function that assigns to each set its cardinality, i.e. the number of members of the set, is a set function.
• The function
• The Lebesgue measure is a set function that assigns a non-negative real number to any set of real numbers, that is in Lebesgue -algebra.
• 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.
• A Random set is a set-valued random variable. See Random compact set.