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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 , .
Defines:
countable additivity,countably additive,$\sigma$-additive,sigma-additive
Synonym:
additivity
Type of Math Object:
Definition
Major Section:
Reference
Mathematics Subject Classification
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new question: Computation of $\varphi(2000)$ by jeremyboden
May 21
new question: pure subgroups by lvoyster
new correction: Typo in M\"obius function? by Aleph Zero
new collection: analytic number theory by Aleph Zero
May 20
new question: Taylor's Series Query! by unlord
new question: Laplace transform by J
new question: Residue Calculus by J
May 19
new Education: Project: PlanetMath Outlines Series by unlord
Info
Corrections
sigma-additive by Koro ✓
positivity by rspuzio ✓
set function pro real function by pahio ✓
countably additive by gel ✓
positivity by rspuzio ✓
set function pro real function by pahio ✓
countably additive by gel ✓
Versions
(v10) by Andrea Ambrosio 2013-03-22


