Refinement of The Notion of Choice Function
A function is said to be a selection of a multivalued map φ:A → B ( that is, a function from A to the power set ), if
The existence of more regular choice functions, namely continuous or measurable selections (see: ) is important in the theory of differential inclusions, optimal control, and mathematical economics.
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“You know that your toddler needed love and approval but he often seemed not to care whether he got it or not and never seemed to know how to earn it. Your pre-school child is positively asking you to tell him what does and does not earn approval, so he is ready to learn any social refinement of being human which you will teach him....He knows now that he wants your love and he has learned how to ask for it.”
—Penelope Leach (20th century)
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