A measure space is a finite measure space if ; it is -finite if the total space is the union of a finite or countable family of sets of finite measure, i.e. if there exists a countable set such that for each , and In this case we also say that is a -finite measure. If is not -finite, we say that it is -infinite.
Examples. Any finite measure space is -finite. A more interesting example is the Lebesgue measure in : it is -finite but not finite. In fact
( is a cube with center at and side length , and its measure is ), but .
|Date of creation||2013-03-22 12:29:48|
|Last modified on||2013-03-22 12:29:48|
|Last modified by||Koro (127)|
|Defines||finite measure space|