tight and relatively compact measures
Tight and relatively compact measuresFernando Sanz
Let be a family of finite measures on the Borel subsets of a metric space . We say that is tight iff for each there is a compact set such that for all . We say that is relatively compact iff each sequence in has a subsequence converging weakly to a finite measure on .
If is a family of distribution functions, relative compactness or tightness of refers to relative compactness or tightness of the corresponding measures.
Let be a family of distribution functions with for all . The family is tight iff it is relatively compact.
Coming soon…(needs other theorems before) ∎
|Title||tight and relatively compact measures|
|Date of creation||2013-03-22 17:19:37|
|Last modified on||2013-03-22 17:19:37|
|Last modified by||fernsanz (8869)|