My Math Forum Probability - Sigma algebra

 June 28th, 2016, 09:29 AM #1 Newbie   Joined: Jun 2016 From: India Posts: 3 Thanks: 0 Probability - Sigma algebra I read in a book "The elements of $\displaystyle sigma$- algebra over a sample space $\displaystyle omega$ are called events" and not all subsets of a sample space are events. Can you please explain this definition?
 June 28th, 2016, 01:47 PM #2 Global Moderator   Joined: May 2007 Posts: 6,511 Thanks: 584 A (set) algebra is a collection of sets (events) which is closed under any finite combination of unions, intersects, and complements, which includes the entire set (sample space). A sigma-algebra extends this notion to include countable combinations as well. Note that measure theory and probability theory are very similar, but the terminology differs: measure theory - sets, probability theory - events.
 June 28th, 2016, 10:47 PM #3 Newbie   Joined: Jun 2016 From: India Posts: 3 Thanks: 0 Actually I a newly studying the probability theory and would like to know why the definition of events is given as following "The elements of a sigma- algebra over a sample omega are called events" and why not all subsets of the sample space of a particular experiment can be events?
 June 29th, 2016, 03:00 AM #4 Senior Member   Joined: Feb 2012 Posts: 144 Thanks: 16 There are two reasons why one considers only set belonging to a sigma-algebra instead of all subsets of Omega. 1) a suitable sigma-algebra is all what is needed. Suppose Omega is the set of real numbers R and X is a real random variable. All the interesting questions you may ask about X is whether X

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