Domain/Measure Theory Definition
Let be a topological space: a valuation is any map
satisfying the following three properties
The definition immediately shows the relationship between a valuation and a measure: the properties of the two mathematical object are often very similar if not identical, the only difference being that the domain of a measure is the Borel algebra of the given topological space, while the domain of a valuation is the class of open sets. Further details and references can be found in Alvarez-Manilla et al. 2000 and Goulbault-Larrecq 2002.
Read more about this topic: Valuation (measure Theory)
Famous quotes containing the words domain, measure, theory and/or definition:
“You are the harvest and not the reaper
And of your domain another is the keeper.”
—John Ashbery (b. 1927)
“Outward simplicity befits ordinary men, like a garment made to measure for them; but it serves as an adornment to those who have filled their lives with great deeds: they might be compared to some beauty carelessly dressed and thereby all the more attractive.”
—Jean De La Bruyère (1645–1696)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)