Example of $\sigma$-algebra
I understood the definition of a $\sigma$-algebra, that its elements are closed under complementation and countable union, but as I am not very good at maths, I could not visualize or understand the intuition behind the meaning of "closed under complementation and countable union".
If we consider the set X to be a finite set, then what would be a good real life example of a $\sigma$-algebra, for a noob to understand.
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$\begingroup$Let $X = \{a, b, c, d\}$, a possible sigma algebra on $X$ is $Σ = \{∅, \{a, b\}, \{c, d\}, \{a, b, c, d\}\}$.
I think this is a good example.
Its power set, i.e. the set $2^X$ (or $\mathcal{P}(X)$ depending on the notations) of all subsets of $X$.
$\endgroup$ $\begingroup$steps to form the smallest sigma field step 1: break the whole space into sets that are mutually exclusive and exhaustive . step 2: then form a new set using these sets(sets obtained in step 1) in this way{ take single sets ,take sum of two at a time ,take sum of three at a time ,..........,take sum of all } . the set so formed is sigma field you need
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