complete measure
A measure space is said to be complete if every subset of a set of measure is measurable (and consequently, has measure ); i.e. if for all such that and for all we have .
If a measure space is not complete, there exists a completion (http://planetmath.org/CompletionOfAMeasureSpace) of it, which is a complete measure space such that and , where is the smallest -algebra containing both and all subsets of elements of zero measure of .
Title | complete measure |
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Canonical name | CompleteMeasure |
Date of creation | 2013-03-22 14:06:56 |
Last modified on | 2013-03-22 14:06:56 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 5 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 28A12 |
Related topic | UniversallyMeasurable |
Defines | completion |
Defines | complete |