Remark

• From (1) and (2)  it follows  that  .
•   is the smallest sigma-algebra formed from the subsets of   .
• If    is a finite set,   then is a sigma-algebra.
• is closed under countable intersection operations also.
               Suppose . Then   and therefore,
                           .

Example 6  Suppose
                        Then the power set   is a sigma algebra.

Example 7  The collection is the smallest sigma algebra containing .          

                         For a finite set ,
                                the power set is the largest sigma algebra containing .