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<infiniti), Ai in A foralli => 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))

source

jl@crush.caltech.edu index

simple_probability_charge

monotone_continuity

probability_charge

probability

utility

savage

QP3

QP2

PA1