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A model's "capacity" property corresponds to its ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity. Two notions of capacity are known by the community. The information capacity and the VC Dimension.
A specific property is the intensive property obtained by dividing an extensive property of a system by its mass. For example, heat capacity is an extensive property of a system. Dividing heat capacity, , by the mass of the system gives the specific heat capacity, , which is an intensive property. When the extensive property is represented by ...
In mathematics, a property is any characteristic that applies to a given set. [1] Rigorously, a property p defined for all elements of a set X is usually defined as a function p: X → {true, false}, that is true whenever the property holds; or, equivalently, as the subset of X for which p holds; i.e. the set {x | p(x) = true}; p is its indicator function.
Many standard Banach spaces have this property, most notably, the space () of continuous functions on a compact space and the space () of the Lebesgue integrable functions on a measure space. Alexander Grothendieck introduced the concept in the early 1950s ( Grothendieck 1953 ), following the work of Dunford and Pettis, who developed earlier ...
A material property is an intensive property of a material, i.e., a physical property or chemical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one material versus another can be compared, thereby aiding in materials selection .
An intensive property does not depend on the size or extent of the system, nor on the amount of matter in the object, while an extensive property shows an additive relationship. These classifications are in general only valid in cases when smaller subdivisions of the sample do not interact in some physical or chemical process when combined.
The creation of express trusts in English law must involve four elements for the trust to be valid: capacity, certainty, constitution and formality. Capacity refers to the settlor's ability to create a trust in the first place; generally speaking, anyone capable of holding property can create a trust. There are exceptions for statutory bodies ...
This example generalizes to other coefficients. Taking rational functions with rational instead of real coefficients produces a countable non-Archimedean ordered field. Taking the coefficients to be the rational functions in a different variable, say , produces an example with a different order type.