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:
“In the domain of art there is no light without heat.”
—Victor Hugo (18021885)
“Poetry is emotion put into measure. The emotion must come by nature, but the measure can be acquired by art.”
—Thomas Hardy (18401928)
“Every theory is a self-fulfilling prophecy that orders experience into the framework it provides.”
—Ruth Hubbard (b. 1924)
“Mothers often are too easily intimidated by their childrens negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)