And indeed, sigma-algebras are a kind of introduction to measure theory (Borel and Lebesgue measures in particular)
]]>http://www.mathisfunforum.com/profile.php?id=148732008-09-30T21:29:06Zhttp://www.mathisfunforum.com/viewtopic.php?pid=97728#p97728The concept of a sigma algebra is particularly useful in analysis. It can actually be quite difficult to prove that any explicit set is (Lebesgue) measurable. However, the set of measurable sets forms a sigma algebra. Using this fact, we can get a whole lot of sets by simply proving that all open and closed sets are measurable. In particular, given those facts any Borel set is indeed measurable.]]>http://www.mathisfunforum.com/profile.php?id=21432008-09-27T23:42:00Zhttp://www.mathisfunforum.com/viewtopic.php?pid=97641#p97641]]>http://www.mathisfunforum.com/profile.php?id=148732008-09-26T18:50:57Zhttp://www.mathisfunforum.com/viewtopic.php?pid=97623#p97623]]>http://www.mathisfunforum.com/profile.php?id=148732008-09-26T18:39:11Zhttp://www.mathisfunforum.com/viewtopic.php?pid=97622#p97622 ]]>http://www.mathisfunforum.com/profile.php?id=67772008-07-31T11:10:20Zhttp://www.mathisfunforum.com/viewtopic.php?pid=95724#p95724 ]]>http://www.mathisfunforum.com/profile.php?id=67772008-07-31T00:48:15Zhttp://www.mathisfunforum.com/viewtopic.php?pid=95693#p95693