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.
Read more about this topic: Choice Function
Famous quotes containing the words refinement, notion, choice and/or function:
“Perhaps our own woods and fields,—in the best wooded towns, where we need not quarrel about the huckleberries,—with the primitive swamps scattered here and there in their midst, but not prevailing over them, are the perfection of parks and groves, gardens, arbors, paths, vistas, and landscapes. They are the natural consequence of what art and refinement we as a people have.... Or, I would rather say, such were our groves twenty years ago.”
—Henry David Thoreau (1817–1862)
“Not so many years ago there there was no simpler or more intelligible notion than that of going on a journey. Travel—movement through space—provided the universal metaphor for change.... One of the subtle confusions—perhaps one of the secret terrors—of modern life is that we have lost this refuge. No longer do we move through space as we once did.”
—Daniel J. Boorstin (b. 1914)
“We must hold a man amenable to reason for the choice of his daily craft or profession. It is not an excuse any longer for his deeds that they are the custom of his trade. What business has he with an evil trade?”
—Ralph Waldo Emerson (1803–1882)
“The fact remains that the human being in early childhood learns to consider one or the other aspect of bodily function as evil, shameful, or unsafe. There is not a culture which does not use a combination of these devils to develop, by way of counterpoint, its own style of faith, pride, certainty, and initiative.”
—Erik H. Erikson (1904–1994)