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October 14th, 2013, 02:10 AM  #1 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  show that [latex]\mu[/latex] is a measure
let be a sigma algebra where how to show that is a measure, where is a measure on ? countable unions? 
October 14th, 2013, 03:21 AM  #2 
Senior Member Joined: Feb 2013 Posts: 281 Thanks: 0  Re: show that [latex]\mu[/latex] is a measure
mu is a measure on M, so mu(empty) = 0 I give a proof for a union of two disjoint sets. I hope you can extend the proof for countable pairwisely disjoint sets. I will detone the new measure by nu. We have to show that nu(EuF u E'uF') = nu(EuF) + nu(E'uF'), where EuF and E'uF' are disjoint sets. The left side is equal with mu(E) + mu(E') by definiton of nu. The right hand side nu(EuF u E'uF') = nu(EuE' u FuF') = nu(EuE' u F'') = mu(EuE') = mu(E) + mu(E') where F'' = FuF' < NuN' = N''. So the two sides are equal. 
October 14th, 2013, 03:30 AM  #3 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  Re: show that [latex]\mu[/latex] is a measure
ah I see it now. Thank you!


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