# generated algebra

• Mar 8th 2011, 07:44 AM
waytogo
generated algebra
Hi,

can anybody explain me how to construct an algebra and $\sigma$-algebra generated by $K$, if $K=\{\{x\}\mid x\in X\}$ and $X$ - universal set.
I guess it also depends on the fact whether $X$ is finite or infinite, countable or uncountable, does it?
• Mar 8th 2011, 12:28 PM
Opalg
Quote:

Originally Posted by waytogo
Hi,

can anybody explain me how to construct an algebra and $\sigma$-algebra generated by $K$, if $K=\{\{x\}\mid x\in X\}$ and $X$ - universal set.
I guess it also depends on the fact whether $X$ is finite or infinite, countable or uncountable, does it?

The algebra generated by $K$ will be the finite subsets of $X$ together with their complements. The $\sigma$-algebra generated by $K$ will be the countable subsets of $X$ together with their complements.