An algebra, A, on a set X satsfies
* empty set in A, X in A
* B in A => comp(B) in A (comp(B) = X/B)
* C,B in A => C union B in A
A sigma algebra, A, on a set X satisfies:
* empty set in A, X in A
* B in A => comp(B) in A (comp(B) = X/B)
* {Ai} 1<=i Union(i=1,infiniti,Ai) in A
Examples:
A={empty set, X}
A=borel sigma algebrea=all open sets
Note that intersection is defined.
A intersct B = Comp(Comp(A) union Comp(B))