PlanetMath: $\sigma$-algebra

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$\sigma$ -algebra

(Definition)

Let be a set. A $\sigma$ -algebra is a collection of subsets of such that

$X\in M$
If $A\in M$ then $X-A\in M$ .
If $A_1,A_2,A_3,\ldots$ is a countable subcollection of , that is, $A_j\in M$ for $j=1,2,3,\ldots$ (the subcollection can be finite) then the union of all of them is also in :

$\begin{displaymath}\bigcup_{j=1}^\infty A_i\in M.\end{displaymath}$

" $\sigma$ -algebra" is owned by drini. [ full author list (2) | owner history (3) ]

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Cross-references: union, finite, countable, subsets, collection
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This is version 4 of $\sigma$ -algebra, born on 2003-10-15, modified 2004-02-26.
Object id is 4835, canonical name is ASigmaAlgebra.
Accessed 1578 times total.

Classification:

28A60 (Measure and integration :: Classical measure theory :: Measures on Boolean rings, measure algebras)

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