Maximal Element - Examples

Examples

  • In Pareto efficiency, a Pareto optimal is a maximal element with respect to the partial order of Pareto improvement, and the set of maximal elements is called the Pareto frontier.
  • In decision theory, an admissible decision rule is a maximal element with respect to the partial order of dominating decision rule.
  • In modern portfolio theory, the set of maximal elements with respect to the product order on risk and return is called the efficient frontier.
  • In set theory, a set is finite if and only if every non-empty family of subsets has a minimal element when ordered by the inclusion relation.

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