additive
Let be some positive-valued set function defined on an algebra of sets . We say that is additive if, whenever and are disjoint sets in , we have
Given any sequence of disjoint sets in A and whose union is also in A, if we have
we say that is countably additive or -additive.
Useful properties of an additive set function include the following:
-
1.
.
-
2.
If , then .
-
3.
If , then .
-
4.
Given and , .
Title | additive |
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Canonical name | Additive |
Date of creation | 2013-03-22 13:00:58 |
Last modified on | 2013-03-22 13:00:58 |
Owner | Andrea Ambrosio (7332) |
Last modified by | Andrea Ambrosio (7332) |
Numerical id | 10 |
Author | Andrea Ambrosio (7332) |
Entry type | Definition |
Classification | msc 03E20 |
Synonym | additivity |
Defines | countable additivity |
Defines | countably additive |
Defines | -additive |
Defines | sigma-additive |