My Math Forum algebra generated by specific family of sets

 Real Analysis Real Analysis Math Forum

 March 8th, 2011, 09:49 AM #1 Member   Joined: Jan 2010 Posts: 44 Thanks: 0 algebra generated by specific family of sets Hi, I have been given a hometask in Measure Theory to describe algebra and $\sigma$-algebra generated by $K$, where $K=\{\{x\}\mid x\in X\}$ and $X$ is the universal set. I think I understand what is algebra and I can recognize it, but I am confused with this. Because it seems that $X$ can be both finite and infinite. And also I am not sure how to cope with countable unions. Can anybody help?
 March 9th, 2011, 06:10 AM #2 Member   Joined: Nov 2009 From: France Posts: 98 Thanks: 0 Re: algebra generated by specific family of sets First of all, $\sigma (K)$ contains all countable subsets of $X$. But $\sigma (K)$ is a $\sigma$-algebra so it contains also their complements. So we can try $\sigma (K):=\left\{A\subset X\mbox{ such that } A \mbox{ is countable or }A^c \mbox{ is countable }\right\}$.

 Tags algebra, family, generated, sets, specific

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post myanthnkz04 Academic Guidance 2 January 17th, 2014 02:35 PM Lolyta Abstract Algebra 1 September 30th, 2013 04:35 AM walter r Applied Math 2 March 13th, 2013 06:51 AM Vasily Applied Math 2 August 19th, 2012 12:31 PM butabi Real Analysis 4 October 3rd, 2010 06:43 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top