# generated algebra

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

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

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