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Unformatted text preview: H as follows: if A = Q \ I 2 H , then m ( A ) = b a if I = ( a;b ) ; [ a;b ] ; ( a;b ] or [ a;b ) : Prove that m is a measure. (c) Prove that the measure m on the semi-ring H is not sigma-additive. 1 Remark : It is assumed that you know the notion of connected set: a set A in a metric space ( M;& ) is called disconnected if there are open sets U;V & M such that (i) A & U [ V; (ii) U \ V = ? ; (iii) A \ U 6 = ? ;A \ V 6 = ? . A connected set is the set which is not disconnected. You can use the theorem stating that a set in R is connected if and only if it is an interval (bounded, unbounded, open, semi-open or closed). 2...
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- Spring '08