extending a capacity to a Cartesian product
Suppose that is a paved space such that is closed under finite unions and finite intersections, and that is a compact paved space. Define to be the closure under finite unions and finite intersections of the paving on .
This result justifies looking at capacities when considering projections from the Cartesian product onto . We see that the property of being a capacity is preserved under composing with such projections. However, additivity of set functions is not preserved, so the corresponding result would not be true if “capacity” was replaced by “measure” or “outer measure”.
Let be -capacitable. Then, is -capacitable.
|Title||extending a capacity to a Cartesian product|
|Date of creation||2013-03-22 18:47:38|
|Last modified on||2013-03-22 18:47:38|
|Last modified by||gel (22282)|