Elements of Statistical Methods Probability (Ch 3) - Statistics

Collection of Events: Required PropertiesAny collection C of events should satisfy the following properties:1. The sample space S is an event, i.e., S ∈ C2. If A is an event, i.e., A ∈ C , so is A c , i.e., A c ∈ C3. For any countable sequence of events, A 1 ,A 2 ,A 3 ... ∈ Ctheir union should also be an event, i.e., S ∞i=1A i ∈ C .Such a collection C with properties 1-3 is also called a sigma-fieldor sigma-algebra.By 1. and 2.: S ∈ C =⇒ S c = /0 ∈ C .C = {/0,S} is the simplest sigma-field.6