This definition is easily shown to be independent of the chosen Hahn decomposition.
It is clear that is a positive measure, and it is called the positive variation of . On the other hand, is a positive finite measure, called the negative variation of . The measure is called the total variation of .
Notice that . This decomposition of into its positive and negative parts is called the Jordan decomposition of .
|Date of creation||2013-03-22 13:27:02|
|Last modified on||2013-03-22 13:27:02|
|Last modified by||Koro (127)|