Hi!

Trying to get a grasp on $\displaystyle \sigma-algebra$.

Letīs say I have a the set $\displaystyle \Omega = \left\{1,2,3}\right\} $.

Now, if I want to find the smallest $\displaystyle \sigma-algebra \, F $ that includes both 1 and 2. Would this be:

$\displaystyle F = \left\{\emptyset, \Omega, 1, 2, 3, \left\{1,2\right\}\right\} $ ?

The empty set is there, and also its complement $\displaystyle \Omega $. Both 1 and 2 are there and their complement 3. Also the union of 1 and 2 are is there.

Thanks!