Posted by J. Holmer on December 12, 2007, 9:16 am, in reply to "measure of a disjoint union of subsets of R^d"
It is possible for the distance between two disjoint sets to be zero. Take the intervals (0,1) and [1,2] in R.
The corollary you describe follows by induction. Here's how you get to three sets, knowing the result for two sets:
m_*(E_1 U E_2 U E_3) = m_*(E_1 U E_2) + m_*(E_3) = m_*(E_1)+m_*(E_2)+m_*(E_3).
115
Message Thread:
« Back to thread