The condition that is increasing means that whenever . Note that capacities differ from the concepts of measures and outer measures, as no additivity or subadditivity conditions are imposed. However, for any finite measure, there is a corresponding capacity (http://planetmath.org/CapacityGeneratedByAMeasure). An important application to the theory of measures and analytic sets is given by the capacitability theorem.
Let be an -capacity on a set . Then a subset is -capacitable if, for each , there exists a such that and .
Alternatively, such sets are called -capacitable or, simply, capacitable.
|Date of creation||2013-03-22 18:47:26|
|Last modified on||2013-03-22 18:47:26|
|Last modified by||gel (22282)|