Sigma algebra

A sigma algebra is an advanced mathematical concept. It refers to a formal mathematical structure intended among other things to provide a rigid basis for axiomatic probability theory.

Examples

Given the set $\Omega$={Red,Yellow,Green}

The power set $2^{\Omega }$ will be {A0,A1,A2,A3,A4,A5,A6,A7}, with

• A0={} (The empty set}
• A1={Green}
• A2={Yellow}
• A3={Yellow, Green}
• A4={Red}
• A5={Red, Green}
• A6={Red, Yellow}
• A7={Red, Yellow, Green} (the whole set \Omega)

Let F be a subset of $2^{\Omega }$: F={A0, A1, A4, A5, A7}.

Notice that the following is satisfied:

1. The empty set is in F.
2. The original set $\Omega$ is in F.
3. For any set in F, you'll find it's complement there also.
4. For any subset of F, the union of the sets therein will also be in F. For example, the union of all elements in the subset {A0,A1,A4} of F is A0 U A1 U A4 = A5.